Since the only lounge would be a Delta SkyClub, the Delta rules ultimately apply (even if you can argue that it doesn't comply with SkyTeam rules, the most you'll get is a sorry a few weeks later, which won't help you).



If we're talking about what DL would consider a stopover (more than 24 hours between arriving and departing ATL), this is likely clearly a no SkyClub access situation
If we're talking about a connection (less than 24 hours): if not an overnight connection, you would have SkyClub access. On an overnight, you wouldn't have access on departure (because of the same-day international flight requirement), but if it's possible to physically access the SkyClub after arriving in ATL (I don't know if that's viable in ATL after CBP) you could argue that you are on a connection from a same-day international flight (whether that argument succeeds is a very good question)

Note that if you have an overnight connection or a more-than-24-hour stopover and really intent on getting to a SkyClub for whatever reason, you could buy a Delta economy ticket departing that evening, which would allow you through TSA to physically get to the SkyClub and would satisfy the connection from same-day international flight requirement (Delta doesn't consider separate tickets disqualifying in this scenario, AFAIK). Since Delta's 24-hour cancel policy for tickets bought directly from Delta effectively means same-day tickets are fully refundable up until time of departure (in fact, Delta just authorizes the charge against your credit card: if you cancel, they don't actually charge your card). If you choose to do this (setting aside the ethical considerations of taking inventory), choosing one of the really short regional flights from ATL (e.g. CSG, which is blocked at as short as 49 minutes) will at least prevent an argument that it makes your next flight impossible. Note that if you make a habit of doing things like this, Delta may be rather displeased with you and the response may not be entirely predictable.