As jthill points out, there is no action that corresponds to compiling in an interpreted language, so in one sense, your question is meaningless. It's like asking, "What's the word for 'claws' on a goldfish?"
But okay, the correct term for what you want is "interprets". And if you think it's awkward to say, "The Lua interpreter interprets the program", then just say, "Lua interprets the program." You'd have the same issue with a compiler. Sure, you could say, "The C compiler compiles the program", but normally we just say, "C compiles the program" or "We compile the C program" or some such. If it's necessary to specify "the Lua interpreter" for some reason, then I guess you could use an alternative word that could be synonymous with "interprets", like "executes" or "processes".
I'd add that while in everyday speech it's common to choose a synonym to avoid sounding repetitious, to give the sentence a certain rhythm, etc, you should be careful about this in technical writing. Many technical terms have precise meanings, and you can't just toss in a synonym because it "flows better". Like, my dictionary says that "drift" is a synonym for "float". But I think it would be a really bad idea to say, "Declare this variable as a drift" because you've already used the word "float" twice in the sentence!