I had to re-bytecode-compile lsp-mode to get it to pick up the faster JSON support (`M-x package-reinstall lsp-mode`). See `lsp-diagnose` for a quick way to check if you're good to go.
Thanks, but I'm using eglot. I might try lsp again, now that some time has passed, though.
Eglot will use the native C JSON parsing if Emacs is compiled with jansson support.