Sort of. Luvi is all the parts that have to be implemented in native C code and not much more. There is some fairly heavyweight code in Lua, such as the HTTP stack (luvi just exposes libuv tcp and TLS from openssl, but no HTTP or websocket code)
Also luvi has the bootstrap code that knows how to read Lua from a zip file. So a luvi based app is the static luvi binary literally concatenated with a zip file containing all the needed Lua code for the app.
Lit is a luvi app as is luvit. lit is the package manager and a toolkit for building luvi based apps. Luvit is a nodejs clone with similar apis built in implemented in Lua and node style APIs.
Personally I don't use luvit much anymore and tend to write my apps directly as luvi based programs using lit to manage deps and package it.