No, the choice of a client/server model was a design decision, one that is not unique to LSP and is also used by some IDEs for various reasons (see, for example, JetBrains Rider). Performance is absolutely fine - the only data that needs to be transferred is that needed to drive the UI, which is trivial over a local socket. Had that not been the case, there are plenty of ways LSP could have been designed as an in-proc library interface and remained just as open as it is.

What makes LSP not 'integrated' in the sense of the I in IDE is the fact that it is decoupled from the editor, allowing one editor to work with many language servers and one language server to work with many editors.