As written elsewhere, the EZE Delta lounge is not really that nice (and that is an understatement).
A few high points:
- No Internet.
- No real food even around mealtimes.
- Not enough seats
- No enforcement of no smoking rules
- Dirty toilets
- No tables to work at.
- VERY crowded. Seats on top of each other with no place to put luggage.
- Uninterested / unehelpful staff.

To be honest, probably better to grab a drink and go sit in the terminal which is spacious and bright.