A Lua-aware startup time profiler

What? The existing common startup time profilers https://github.com/dstein64/vim-startuptime and https://github.com/tweekmonster/startuptime.vim do not report timing information for Lua files. This would be helpful to have.

Why? Startup timing information that includes Lua files in the time breakdown is useful for tuning one's configuration.

Potential existing implementations: Building off of one of the common startup time profilers could be useful.

Potential pitfalls: This seems like it may require changes to Neovim's built-in startup time profiling, to ensure that Lua files are included in the output. I think that the common profiling plugins just parse this output, so it's plausible that simply augmenting the output would allow them to include Lua timing without modification.