I wanted to do some research but i could not find any information about this topic.
The only information that i found -> http://benchmarksgame.alioth.debian.org/u32/compare.php?lang=csharp&lang2=lua
And I'm not sure how i can interpret this chart. If I'm right it basicly says that Lua is 10times faster than Mono. But Mono's memory usage is ~8 times better than Lua.
What does this say about perfomance ?
Comparing Lua with Mono -> Advantages/Disadvantages
Edit: [Gamedevelopment] Cryengine 3 uses c++/lua atm. But some guys releasing a mono port for this engine. I'm very familiar with Mono. But now i wanted to do some research on Lua to see if its worth to learn this language or if I should stick with Mono
You're comparing apples to oranges. C# is a statically typed language, compiled to CIL which is a bytecode language, run (or usually JITted) by a virtual machine, and used for web and standalone application development. Lua is a dynamically typed scripting language typically run by an interpreter, often embedded as an extensible scripting language into a larger application.
Also, your interpretation of the benchmark is wrong. The bar chart shows that the Mono program takes around 1/10th of the time to run compared to an equivalent Lua program.
That said, this kind of microbenchmark is largely useless. Don't take my word for it; read what the Shootout itself has to say about it. You should read the whole thing, but I'll pull out some juicy citations:
Long story short: select your language based upon whether it does well at what you want to do with it, whether it lets you express your intent clearly, whether it lets you write clean, maintanable code; not based upon some largely meaningless numbers.