Yes, you can control a namespace (in the form of a table, of course) in which a module you require executes. The global definitions are then placed in the table. You can implement copy-on-write using this namespace and a metatable, you can change the semantics of accessing an uninitialized (global) variable, etc. Lua is incredibly flexible, after all. Unfortunately, since you have to implement (and then maintain!) those yourself, it's hard to justify (IME) using Lua instead of a more full-featured solution (that might still incorporate Lua somewhere in the stack[0]), esp. since the main selling point of Lua is simplicity.
[0] You can use something like Fennel or Haxe to compile a more structured language to Lua, or you can use an alternative implementation like Luau.
[0] You can use something like Fennel or Haxe to compile a more structured language to Lua, or you can use an alternative implementation like Luau.