LSP requires two entities: A language server and a language client. The LSP Language Server(LS) implementation for Ballerina is included in the Ballerina distribution(https://ballerina.io/downloads/). According to the LSP(https://microsoft.github.io/language-server-protocol/overviews/lsp/overview/), there should be a separate LSP language client for each editor. Atm, we only have a language client for VSCode in the form of Ballerina VSCode extension. It has a LSP language client which communicates with the Ballerina LS.
Therefore, you have to develop a new Language Client (extension) for the desired editor to use the Ballerina LS there.
The Ballerina LS is not published as a separate artifact. However, ballerina-lang can be built from source as specified in https://github.com/ballerina-platform/ballerina-distribution/blob/master/docs/build-ballerina-from-source.md. You can use the resulting jar to invoke the Ballerina LS from the the developed Language Client. I am happy to help if you need more information on how to develop a Language Client.