The language server protocol is diametrically opposite to the way that IntelliJ works. For each language, IntelliJ builds its own internal representation (PSI) of the source code. There are a lot of language specific things, but there are also a lot of commonalities between languages.
I have no idea how you would morph (say) IntelliJ's Java support to use a LSP without basically throwing everything away and starting over.
Caveat: I never worked at Jetbrains, but I did work for two years supporting Android Studio and IntelliJ at Google, which involved a lot of work in its internals.