Kinda.

Lua defines it implicitly only when you use the

function foo:bar(a, b, c) -- note the colon

syntactic sugar, which gets translated to

function foo.bar(self, a, b, c) -- note the period

In all cases, self is a regular variable name. You can even redeclare a new local with that name even when the old one is in scope.

Edit: some typos