how are Updates and Deletes handled in both Data Warehouses and Data Lakes?

Question

I'm trying to understand how Update and Delete functions are performed in Data Warehouses, Lakes and Lakehouses.

Databricks argues that they can perform upserts easily, which I would understand as adding CRUD capabilities.

I've read elsewhere that data lakes only get CR, and warehouses CRU.

Is this correct? how are Updates and Deletes handled in both Data Warehouses and Data Lakes?