I've been following the book Crafting Interpreters which makes a language slightly similar to lua but with bracketed blocks and other small changes. This is a stack based interpreter which feels like a great place to start. There's also register based which seems to use more of a word code to bytecode approach but couldn't tell you much else the differences. I'd highly recommend building an interpreter first as this is a virtual machine and you can make your own fake assembly with less consequences. Writing a real native code compiler is a lot harder if you don't have that baseline under your belt, but you do you if you're confident in your knowhow!
I guess the biggest takeaway i've come across is you can make functions without too much headache, but closures are much harder, you need to move local variables off the stack and onto the heap. Not sure how register handles it
Lua does intrinsic evaluation of strings that i'd argue is not nearly as crazy. I get the value of it since half of interpreted languages it just churning through strings. But I also don't recommend any large codebase ever use JS's == or string coercion because it can go against expectations. This graph argues in JS's favor but comparison is a little more crazy https://algassert.com/visualization/2014/03/27/Better-JS-Equality-Table.html