lsp: explicitly drop locks in handle_input (#12276)

Due to lifetime extension rules, we were holding onto the request
handler map mutex during parsing of the request itself. This had no
grand repercussions; it only prevented registering a handler for next
request until parsing of the previous one was done.



Release Notes:

- N/A
e5085dfef6Piotr Osiewicz committed on 5/25/2024, 10:25:17 AM· committed by GitHubparent32f11df
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