[myrroddin]

In the initial example, since the function is called over and over many times, I would think

local newVar = UPVALUE_VAR
local function MyFunction()
    -- do something with newVar
end

Would be much better than

local function MyFunction()
    local newVar = UPVALUE_VAR
    -- do something with newVar
end

Simply because you are assigning newVar once rather than repeatedly, especially since its value never changes. That said, is assigning upvalues a performance gain? That's a different story.