The listed benefits for SE just say the regular Business Class lounge in DXB; no mention of the First Class Lounge, though it could have been one of those un-publicly-documented things (like, eg. meal selection priority). Perhaps it's only SE-MM who get access without invite-only super-premium cards?

I also was mistaken in my (mis-)recollection of a reciprocal arrangement with Emirates for the Signature Suite (SS) --> First Class passengers only there.