Can't be done in any reasonable way. For an example of why, look at this:
function makefunction(name)
local a = 1
local b = 2
local c = 3
-- ...
return assert(loadstring("return " .. name))
end
local a = 4
local func = makefunction("a")
print(func())
If this worked, what is printed? 1 or 4? Does it capture the variable from the place where the function was loaded, even though that function doesn't exist anymore? Or does it look it up from the place where it was called?
The first would mean that the function is lexically scoped wherever it's created. Being able to access the variable after the function has exited means that the variable would need to be promoted into an upvalue dynamically, which is not something that Lua can do at the moment. As it is now, Lua can see every access to a local variable during compilation, so it knows which variables to turn into upvalues (at a performance hit) and which to keep as locals.
The second would mean that variable accesses inside a loadstring'd function would work completely different than every other access in Lua: Lua uses lexical scoping, not dynamic scoping. It'd be a huge implementation change in Lua, and an extremely inconsistent one.
So, neither is supported. You can control the environment of a dynamically loaded function, using setfenv in Lua 5.1 or the env parameter of load(...) in Lua 5.2, but neither of those let you access local variables automatically.