Last week, I was traveling JFK-MXP on AZ. I went to all three T1 Skyteam lounges, as I wanted to experience what they had to offer, as well as their differences.

T1
Air France lounge - by far the best of the Skyteam lounges. Recent renovations occurred last summer/fall. It's a nice, spacious interior. Despite my traveling on AZ, the lounge attendants didn't attempt to shoo me away. They advised me that they wouldn't alert me to boarding times, since I was flying on AZ. The food offerings are plentiful and fresh. Lots of hot entrees like soups, noodles, quiche, beef bourguignon. Breads, salads and cheeses. Beverage selection was fantastic...alcohol selection was good too. Wifi worked well. I did enjoy the use of real silverware and glass, in lieu of plastic, that Delta uses.

Alitalia lounge was just ok. Lots of leather sofas (welcome to Italy). They have Rai Uno blaring on the TV monitors. I did enjoy the selection of food, although it was not as good as AF. They have individual packaged foods like pasta and sandwiches. There is also a wide selection of chips and crackers. Lots of beverage options, although I didn't particularly enjoy the plastic cups or plastic silverware.

Korean Airlines: The worst of all Skyteam lounges in T1. This is a tiny space. Aeroflot also uses this lounge, so it gets crowded. Food offerings consisted of chips and crackers, costco sandwiches and instant ramen. Beverages were standard.

T4 - Delta Skyclub. Underwhelming, after being in Europe. In fact, it's quite ghetto inside this "gem" of Delta's skyclubs. How can Delta market this lounge as a premium experience when their food offerings are SO paltry. Chex snack mix and carrot sticks? Please! I did enjoy the recent addition of chicken salad.....at least it's better than it was in December.

If there's an extra nickel to be drained, you better believe Delta will find it....meh

If you're flying DL out of T4, I don't think you'll get past security in T1. They don't accept DL boarding passes. I was flying on 006 ticket stock and I had to get an AZ boarding pass to be permitted past T1 security.

Unfortunately for the OP, you're only choice will be T4 Delta Skyclub.