Would it be 200 lines of Java? It'd be 200 lines of just for the boilerplate. It isn't really a selling point of Clojure because it is subjective, but low-syntax high-terseness look of the code is in itself a reward for using the language.
And there isn't anything especially wrong with sticking to Java primitives if someone is comfortable with them. They work fine for Java programmers. The dude doesn't need to learn a new async library to write an LSP client if he doesn't feel like it. Code works, its easy to read, easy to understand and modify.
Line count is not very useful to compare without the context of standard library size, third-party dependencies, etc. The code in TFA depends[1] on a JSON library[2] that is about a thousand lines of code (excluding tests) wrapping a Java library for JSON decoding.
Then there's other things to consider, like the fact that this LSP client, while succinct, pays not only the cost of loading Jackson, but also the cost of loading clojure.core, which is quite non-trivial[3]. Startup time for LSP servers and clients definitely matters to some, considering that e.g. even clojure-lsp recommends running native executables over JAR files[4]. Can't find documentation proving it's for quick startup, but it's a plausible rationale for their recommendation of a binary over a JAR.
Note: I have used Clojure professionally and in hobby projects. I think it's nice that one can interactively develop a minimal LSP client and the resulting amount of work is roughly 200 lines of code. I say "minimal" because it's unclear how this client deals with offsets reported by LSP servers, which are all given as offsets in a UTF-16 encoded string. In any case, I still think advertising "LSP client in 200 lines of code" hides valuable information regarding functionality, implementation, "actual" code size, and trade-offs made in the choice of technology stack.
And there isn't anything especially wrong with sticking to Java primitives if someone is comfortable with them. They work fine for Java programmers. The dude doesn't need to learn a new async library to write an LSP client if he doesn't feel like it. Code works, its easy to read, easy to understand and modify.