Delta doesn't have a first class cabin, but I assume you are referring to their business class seats. Currently, the majority of their international fleet does not have lie-flat seats, however they in the process of installing lie-flat seats on their entire international fleet. As for transatlantic specifically, the only markets that i am aware of that have dedicated lie-flat seats are all flights into LHR and the ATL-DXB and ATL-JNB routes (there might be a few others but these are the ones I know of and of course as planes rotate other markets see lie-flats occasionally).
If you're flying on the A330, then you're going to get an ex-NW angled-lie-flat seat. If you're flying on the 767 then you are most likely to get one of the old recliners which DL are phasing out over the next few years.