There are a number of build systems that can use Lua, based strongly on Lua or even implemented in Lua. Some of them are listed at the Lua User's Wiki.
Of the ones listed at the wiki, Bou was explicitly inspired by Rake. Its author observed that the name "lake" was already in use for another build system, but didn't provide a link so I have no clue what that one might have been related to.
The "official" binary releases of Lua all come from a system called tecmake originated at Tecgraf like Lua itself. Tecmake is implemented on top of make, via a wrapping shell script and a common set of Makefile rules implementing its conventions. It works well for them, but personally I've never been able to get it to run on my system.
LuaRocks uses Lua to describe build requirements, is written almost entirely in Lua, and is intended to be integrated with a distributed application so that applications can be self-updating. I don't know how easy it would be to leverage its build engine for other purposes, but I'm sure it could be done.