Does Mel, Newly Awakened's empower work with Ahri Legend?

No. Mel's empowered ability reads, "If a spell or ability you control would give -[S] to a unit it chooses, it gives an additional -1[S]." Ahri's legend gives -1 Might to an attacking unit automatically — it never chooses a unit. The controller has no selection; the affected unit is programmatically identified by the trigger condition (the unit that attacked). Per Rule 355.10.d, that means it's not a choice, so Mel's condition is not met. Ahri gives -1; Mel stays silent.