(Lean has a somewhat different type theory from Coq, where propositions in Prop have the property that all proofs of a property are defined to be equal. It turns out this along with functional extensionality (that two functions are equal iff their evaluations are all equal) is enough to get LEM, but only in Prop. Outside Prop there's a stronger commitment to constructibility. Still, every definition and lemma has some program backing it.)
I wouldn't really say that it has a different type theory, just that it has proof irrelevance and functional extensionality build into the kernel as axioms. But yeah, it's a good way to show that you definitely don't have to give up LEM.
(Lean has a somewhat different type theory from Coq, where propositions in Prop have the property that all proofs of a property are defined to be equal. It turns out this along with functional extensionality (that two functions are equal iff their evaluations are all equal) is enough to get LEM, but only in Prop. Outside Prop there's a stronger commitment to constructibility. Still, every definition and lemma has some program backing it.)