Tree-sitter and LSP solve different problems.

LSP is a full fledged semantics solution providing go-to-definition functionality, trace references, type info etc. But requires a full language server, project configuration, and often a working build. That's great in an IDA, but the burden could be a bit much when it comes to working through an agent.

Tree-sitter handles structural queries giving the LLM the ability to evaluate function signatures, hierarchies and such. Packing this into the recursive language model enables the LLM to decide when it has enough information, it can continue to crawl the code base in bite sized increments to find what it needs. It's a far more minimal solution which lets it respond quickly with minimal overhead.

LSP is designed to help editors, not AI agents, and provides query by cursor position. Treesitter supports query by symbol (find definition, usages, etc), and so is much better suited to what an AI agent may want to do.