I have made some progress with this, using into_actor().spawn(), but I am struggling to access the ctx variable inside the async block.
I'll start with showing a compiling snippet of the web socket handler, then a failing snippet of the handler, then for reference the full code example.
Working snippet:
Focus on the match case Ok(ws::Message::Text(text))
/// Handler for `ws::Message`
impl StreamHandler<Result<ws::Message, ws::ProtocolError>> for MyWebSocket {
    fn handle(&mut self, msg: Result<ws::Message, ws::ProtocolError>, ctx: &mut Self::Context) {
        // process websocket messages
        println!("WS: {:?}", msg);
        match msg {
            Ok(ws::Message::Ping(msg)) => {
                self.hb = Instant::now();
                ctx.pong(&msg);
            }
            Ok(ws::Message::Pong(_)) => {
                self.hb = Instant::now();
            }
            Ok(ws::Message::Text(text)) => {
                let future = async move {
                    let reader = processrunner::run_process(text).await;
                    let mut reader = reader.ok().unwrap();
                    while let Some(line) = reader.next_line().await.unwrap() {
                        // ctx.text(line);
                        println!("line = {}", line);
                    }
                };
                future.into_actor(self).spawn(ctx);
            }
            Ok(ws::Message::Binary(bin)) => ctx.binary(bin),
            Ok(ws::Message::Close(reason)) => {
                ctx.close(reason);
                ctx.stop();
            }
            _ => ctx.stop(),
        }
    }
}
Not working snippet with ctx line uncommented.
/// Handler for `ws::Message`
impl StreamHandler<Result<ws::Message, ws::ProtocolError>> for MyWebSocket {
    fn handle(&mut self, msg: Result<ws::Message, ws::ProtocolError>, ctx: &mut Self::Context) {
        // process websocket messages
        println!("WS: {:?}", msg);
        match msg {
            Ok(ws::Message::Ping(msg)) => {
                self.hb = Instant::now();
                ctx.pong(&msg);
            }
            Ok(ws::Message::Pong(_)) => {
                self.hb = Instant::now();
            }
            Ok(ws::Message::Text(text)) => {
                let future = async move {
                    let reader = processrunner::run_process(text).await;
                    let mut reader = reader.ok().unwrap();
                    while let Some(line) = reader.next_line().await.unwrap() {
                         ctx.text(line);
                        println!("line = {}", line);
                    }
                };
                future.into_actor(self).spawn(ctx);
            }
            Ok(ws::Message::Binary(bin)) => ctx.binary(bin),
            Ok(ws::Message::Close(reason)) => {
                ctx.close(reason);
                ctx.stop();
            }
            _ => ctx.stop(),
        }
    }
}
Full code snippet split over two files.
main.rs
//! Simple echo websocket server.
//! Open `http://localhost:8080/ws/index.html` in browser
//! or [python console client](https://github.com/actix/examples/blob/master/websocket/websocket-client.py)
//! could be used for testing.
mod processrunner;
use std::time::{Duration, Instant};
use actix::prelude::*;
use actix_files as fs;
use actix_web::{middleware, web, App, Error, HttpRequest, HttpResponse, HttpServer};
use actix_web_actors::ws;
/// How often heartbeat pings are sent
const HEARTBEAT_INTERVAL: Duration = Duration::from_secs(5);
/// How long before lack of client response causes a timeout
const CLIENT_TIMEOUT: Duration = Duration::from_secs(10);
/// do websocket handshake and start `MyWebSocket` actor
async fn ws_index(r: HttpRequest, stream: web::Payload) -> Result<HttpResponse, Error> {
    println!("{:?}", r);
    let res = ws::start(MyWebSocket::new(), &r, stream);
    println!("{:?}", res);
    res
}
/// websocket connection is long running connection, it easier
/// to handle with an actor
struct MyWebSocket {
    /// Client must send ping at least once per 10 seconds (CLIENT_TIMEOUT),
    /// otherwise we drop connection.
    hb: Instant,
}
impl Actor for MyWebSocket {
    type Context = ws::WebsocketContext<Self>;
    /// Method is called on actor start. We start the heartbeat process here.
    fn started(&mut self, ctx: &mut Self::Context) {
        self.hb(ctx);
    }
}
/// Handler for `ws::Message`
impl StreamHandler<Result<ws::Message, ws::ProtocolError>> for MyWebSocket {
    fn handle(&mut self, msg: Result<ws::Message, ws::ProtocolError>, ctx: &mut Self::Context) {
        // process websocket messages
        println!("WS: {:?}", msg);
        match msg {
            Ok(ws::Message::Ping(msg)) => {
                self.hb = Instant::now();
                ctx.pong(&msg);
            }
            Ok(ws::Message::Pong(_)) => {
                self.hb = Instant::now();
            }
            Ok(ws::Message::Text(text)) => {
                let future = async move {
                    let reader = processrunner::run_process(text).await;
                    let mut reader = reader.ok().unwrap();
                    while let Some(line) = reader.next_line().await.unwrap() {
                        // ctx.text(line);
                        println!("line = {}", line);
                    }
                };
                future.into_actor(self).spawn(ctx);
            }
            Ok(ws::Message::Binary(bin)) => ctx.binary(bin),
            Ok(ws::Message::Close(reason)) => {
                ctx.close(reason);
                ctx.stop();
            }
            _ => ctx.stop(),
        }
    }
}
impl MyWebSocket {
    fn new() -> Self {
        Self { hb: Instant::now() }
    }
    /// helper method that sends ping to client every second.
    ///
    /// also this method checks heartbeats from client
    fn hb(&self, ctx: &mut <Self as Actor>::Context) {
        ctx.run_interval(HEARTBEAT_INTERVAL, |act, ctx| {
            // check client heartbeats
            if Instant::now().duration_since(act.hb) > CLIENT_TIMEOUT {
                // heartbeat timed out
                println!("Websocket Client heartbeat failed, disconnecting!");
                // stop actor
                ctx.stop();
                // don't try to send a ping
                return;
            }
            ctx.ping(b"");
        });
    }
}
#[actix_web::main]
async fn main() -> std::io::Result<()> {
    std::env::set_var("RUST_LOG", "actix_server=info,actix_web=info");
    env_logger::init();
    HttpServer::new(|| {
        App::new()
            // enable logger
            .wrap(middleware::Logger::default())
            // websocket route
            .service(web::resource("/ws/").route(web::get().to(ws_index)))
            // static files
            .service(fs::Files::new("/", "static/").index_file("index.html"))
    })
    // start http server on 127.0.0.1:8080
    .bind("127.0.0.1:8080")?
    .run()
    .await
}
processrunner.rs
extern crate tokio;
use tokio::io::*;
use tokio::process::Command;
use std::process::Stdio;
//#[tokio::main]
pub async fn run_process(
    text: String,
) -> std::result::Result<
    tokio::io::Lines<BufReader<tokio::process::ChildStdout>>,
    Box<dyn std::error::Error>,
> {
    let mut cmd = Command::new(text);
    cmd.stdout(Stdio::piped());
    let mut child = cmd.spawn().expect("failed to spawn command");
    let stdout = child
        .stdout
        .take()
        .expect("child did not have a handle to stdout");
    let lines = BufReader::new(stdout).lines();
    // Ensure the child process is spawned in the runtime so it can
    // make progress on its own while we await for any output.
    tokio::spawn(async {
        let status = child.await.expect("child process encountered an error");
        println!("child status was: {}", status);
    });
    Ok(lines)
}
Error:
error[E0495]: cannot infer an appropriate lifetime due to conflicting requirements
  --> src/main.rs:57:41
   |
57 |                   let future = async move {
   |  _________________________________________^
58 | |                     let reader = processrunner::run_process(text).await;
59 | |                     let mut reader = reader.ok().unwrap();
60 | |                     while let Some(line) = reader.next_line().await.unwrap() {
...  |
63 | |                     }
64 | |                 };
   | |_________________^
   |
note: first, the lifetime cannot outlive the anonymous lifetime #2 defined on the method body at 45:5...
  --> src/main.rs:45:5
   |
45 | /     fn handle(&mut self, msg: Result<ws::Message, ws::ProtocolError>, ctx: &mut Self::Context) {
46 | |         // process websocket messages
47 | |         println!("WS: {:?}", msg);
48 | |         match msg {
...  |
74 | |         }
75 | |     }
   | |_____^
note: ...so that the types are compatible
  --> src/main.rs:57:41
   |
57 |                   let future = async move {
   |  _________________________________________^
58 | |                     let reader = processrunner::run_process(text).await;
59 | |                     let mut reader = reader.ok().unwrap();
60 | |                     while let Some(line) = reader.next_line().await.unwrap() {
...  |
63 | |                     }
64 | |                 };
   | |_________________^
   = note: expected  `&mut actix_web_actors::ws::WebsocketContext<MyWebSocket>`
              found  `&mut actix_web_actors::ws::WebsocketContext<MyWebSocket>`
   = note: but, the lifetime must be valid for the static lifetime...
note: ...so that the type `actix::fut::FutureWrap<impl std::future::Future, MyWebSocket>` will meet its required lifetime bounds
  --> src/main.rs:66:41
   |
66 |                 future.into_actor(self).spawn(ctx);
   |                                         ^^^^^
error: aborting due to previous error
For more information about this error, try `rustc --explain E0495`.
cargo
[package]
name = "removed"
version = "0.1.0"
authors = ["removed"]
edition = "2018"
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
[dependencies]
tokio = { version = "0.2", features = ["full"] }
actix = "0.10"
actix-codec = "0.3"
actix-web = "3"
actix-web-actors = "3"
actix-files = "0.3"
awc = "2"
env_logger = "0.7"
futures = "0.3.1"
bytes = "0.5.3"
 
                        
Here are the basics. You may need to do a little work here and there but this works.
Running
lsLooks like this.