to the best of my understanding, the bottom line when it comes to lounge access has to do with your status in one particular alliance (e.g. *A, SkyTeam) and the carrier you're flying (e.g. what metal you're flying, not what ticket stock you're holding).

one major perk for being a *A Gold is the ability to use any *A lounge (with some exceptions, such as the SKL in SIN) whenever you're holding a ticket to travel on a *A int'l flight that day. doesn't matter what cabin you're in, and doesn't matter which lounge you want to use.

the perk is different for those traveling in C or F when it comes to lounge access on the day of travel...you're entitled to use the lounge of the airline you're flying out of that airport that day. Just because SQ is a member of the *A, flying in F for the other legs of your journey doesn't give you an all-access pass to any *A lounge worldwide that day, just as a *A Gold traveling on your same itinerary on NW/KL instead of SQ, for example, wouldn't have access to any of SkyTeam's (CO/DL/KE/AZ/SU, etc) lounges that day either.

while you're itinerary involves F class travel on a *A carrier, without being a *A Gold member, your only privilege is having access to that carrier's lounge (or whichever lounge they make available to their pax traveling in F/C). So let's say you had a layover in FRA for several hours, in your case you would only have access to SQ's lounge (or whichever lounge they use)--you would not be entitled to use any other *A lounge at your discretion (e.g. LH, UA, etc) because you don't have *A elite privileges.

So regarding your original question, the only lounge you will have access to in ATL is the DL lounge, and if i'm not mistaken, the lounges of any SkyTeam members (CO, NW, etc). Assuming SQ had a lounge in ATL, you wouldn't even be granted access to their lounge in ATL unless you were departing ATL on a SQ flight, even though you'll be flying in F with them on the next leg of your journey (I learned this on my recent trip to Thailand, which made me revise my itinerary--I flew LAX-SIN on SQ but was scheduled to go SIN-BKK on TG, and even though I'm a *A Gold and I would have just arrived after a biz class flight on SQ, I would not have been allowed entry to the SQ SKL in SIN--I would have only had access to the TG lounge in SIN because of this policy. Needless to say, I changed my SIN-BKK flight to a SQ flight instead so that I would have SKL access in SIN during my long layover. Indeed, this rule was strictly enforced...many turned away, and only pax on flights departing SIN on SQ in C/F were allowed in along with a few others who are granted access, like LH senator members if i'm not mistaken).

To get back to my point, in ATL, you technically are simply a pax traveling on int'l F, with your first leg on a DL flight--and that's all that matters--not on what carrier or where to you're traveling after--and will be welcomed in the above mentioned lounges. Without *A status, you will have no access to any *A lounge. The LH lounge is probably crowded enough with its own C and F pax, along with all of the UA and US *A Gold pax traveling int'l that day on different *A flights, and I don't think you'd be granted access if you were connecting in JFK to a flight to FRA on LH in F. (but, you would get access to the LH lounge in JFK...)

Long winded answer, I know, but your only options at ATL are going to be DL and the SkyTeam lounges. In every other city you're going to, you'll have access to the respective lounge of whatever carrier you're flying to your next destination, and depending on the rules, perhaps some SkyTeam lounges as well, but only because of your DL status--it wouldn't have anything to do with your itinerary that day. Once you're in JFK, you're a guest of SQ for the rest of your journey. When you return, if you're flying JFK-ATL on DL, the same rule will apply in JFK--your journey as a SQ pax has technically ended and from that point forward you'll only have access to DL/SkyTeam lounges...not *A lounges.

The rules for *A and SkyTeam elite are very similar when it comes to lounge access, so I'm sure you understand why it's a coveted perk and why members of each alliance like the way the rules are set up. i think if it were any other way, there wouldn't be the same allure and incentive of remaining loyal to one alliance over another. it's great that you can fly SQ with DL miles, just as it's great that you can fly QA with CO miles, but when you fly on partner awards and not alliance awards, the benefits of being loyal to one carrier and one alliance become much more conspicuous.

hope this helps...