Adding a post May 1 / post ITA update for anyone who may find this via search.
Plaza Premium is now the contract lounge for departing D1 pax. It is also a Priority Pass lounge (sign stated 2 hours max stay).
While arriving DL pax can physically get to the door of the lounge (DL arrivals are airside), neither a D1 ticket or Priority Pass allow access on arrival.
The Plaza Premium lounge is in the upper level/mezzanine of Boarding Area E1-8. DL typically operates out of the adjacent pier (Gates E11-E15 or so). The lounge is not particularly easy to find the first time. Attached a few pictures below.
This is the entrance to the section of T3 where the lounge is. This is closest to the DL gates...if you are originating in FCO you will likely come up another set of escalators at the other end. Those escalators are directly in front of you after you exit Duty Free.
If you are originating in FCO, after you exit Duty Free and go up the escalators, turn around and the lounge will be directly in front of you and to your right.