I believe that the goal of the existing efforts to implement Language Server Protocol in Processing is to make it easier to integrate Processing in other development environments. To cite Ben again:
This would allow Processing to work with other editors, reducing the stress on the PDE needing to support every last detail that advanced users seek. [source]
Initial work now incorporated for Processing 4.1. (…) we don’t have an official client yet, but hopefully the community can help fill that hole for various platforms for at least the time being. [source]
So if you have the time, motivation, and skills, it may be most productive to help improve the existing LSP implementation, or prototype an LSP client for your favorite editor. See for reference:
- Implementation language server by kgtkr · Pull Request #564 · benfry/processing4 · GitHub
- Language Server for VS Code and others · Issue #117 · benfry/processing4 · GitHub
That said, as @svan said, if you have a strong drive to build your own code editor from scratch, by any means, go ahead 
I’m sure you’ll learn a lot from the experience.