As someone who has implemented a fair few DSLs, lexical and syntactic analysis is pretty much the same anywhere, and the structure of the lexer/parser does not really depend on the grammar of the language.

And even semantic analysis is at least very similar in most PLs. Even DSLs. Assuming you're using concepts like variables and functions.

When it comes to codegen / interpreter runtimes, things start to diverge. But this also depends on the use case. More often than not a DSL is a one-to-one map to an existing language, with syntactic sugar on top.

I'm curious, what's the DSL you're working on?