If you're FB Gold, and you're travelling on the same DL-coded flights, you should both get lounge access in both MAN and ATL:
The following service benefits are available on all Delta Air Lines-operated flights with a SkyTeam prefix:
Lounge access including one guest* [Gold, Platinum]
* You have access to the lounge when you fly on:
a domestic SkyTeam flight with a connection to an international SkyTeam flight on the same day.
an international AIR FRANCE, KLM, Aircalin or SkyTeam flight.
SkyTeam Elite Plus members, regardless of their travel class, are allowed access to a SkyTeam lounge at a particular airport if traveling on or connecting to/from a same-day international flight operated by a SkyTeam member airline. Simply present your same-day ticket for an international SkyTeam airline flight and a valid Elite Plus membership card.
In addition, SkyTeam Elite Plus members are allowed to invite a guest, who is also traveling on a flight operated by a SkyTeam member airline, to join them in the lounge.