I'd love to see Lua have something like Typescript. I wrote the Haxe target for Lua, but they're fairly different syntactically (echoing the situation for Haxe and _javascript_). Still, it's nice using some of the Haxe ecosystem libraries for Lua now.
Having a compiler in the loop can catch simple errors, reduce generated filesize, and help gloss over differences in Lua versions. However, I think special care must be taken to make it fast to compile. I think typescript lacks a bit in this regard, especially for larger projects (which is where typescript *should* shine). I'd strongly recommend OCaml for writing a typescript-like compiler for Lua. It's what we used for Haxe, and as a result it's fantastically fast.
The wild thing about Lua is that it keeps finding itself in the middle of new and exciting tech... whether it's machine learning in Torch, or super fast web frameworks with nginx. The folks coming to Lua from those domains have very different expectations and experiences than folks doing embedded or game scripting. It's up to the Lua community to decide if it embraces those communities, or if it sticks to its original culture.