Is it not possible to utilize the lua LSP in neovim?

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Yes, it is possible to utilize the lua LSP in neovim. Neovim has built-in support for LSP, including the ability to use external LSP servers such as the lua LSP. To use the lua LSP in neovim, you can install the lua-language-server using your package manager or clone the repository, and then add the server to your neovim configuration. Here is an example configuration:

" Language server setup
if executable('lua-language-server') == 1
  au User lsp_setup call lsp#register_server({
        \ 'name': 'lua',
        \ 'cmd': {server_info->['lua-language-server']},
        \ 'whitelist': ['lua'],
        \ })
endif

This configuration will register the lua-language-server as a server for the lua language and add it to the neovim LSP registry.