Take me out for lunch? Too late - just saw this at nearly 2am and already busy!

EZE bag storage, going to the city, going back to EZE, and then going to AEP is not practical.

No arrival EZE lounges. I'd look for a cheap room in or around the Microcentro and just leave at 10pm or so and head to AEP. As a practical matter, you won't get to the City until 530 earliest with a 4p EZE arrival, and should arrive AEP no later than 10p. I'd also suggest that you talk to one of the remise services upon arrival at EZE to see if a driver will take you on a city tour with your luggage in the trunk, etc. Too late to suggest anyone that I might recommend. at this point. Figure that you really have 4 hours to kill.

Weather is lovely here - you just missed the torrential flooding.