[0] https://luajit.org/ext_ffi.html
The language implementation is fast, and allows you to tap into any C-compatible library.
The question isn't why you would go through Lua, but why you would choose something with less support?
That's the role of the C API [0]. But usually you'd just be passing C up to Lua to bind it together.
[0] https://luajit.org/ext_c_api.html
[0] https://luajit.org/ext_ffi.html