Any relationships you have don't matter once divorce and/or seperation papers are filed. If you try to hide Gym Lady, that sends up red flags. Because ex admitted to having a girlfriend it was no big deal.
If your lawyer is deposing her and the SSLBPOS isn't that done in the lawyer's office? I'm sure a subpeona would get the SSLBPOS's attention since that is transcribed. Does that mean they'll depose you, too?
Was your spouse aware of you trying to "check out"? You could always do a consult saying you're considering divorce with a different attorney and ask him/her that question. Once your lawyer knows it effects their direction. That's vital to know.
What actions did you take after your attempt? Were you under medical care, counseling, etc? People can do pretty destructive things to themselves when faced with major emotional upheaval. What's done afterward can make the biggest impression.
Only you can decide what to tell Gym Lady. You're still legally married/separated. Your emotions go through another loop once the divorce heats up and another when it is final. If it bugs you that much, tell her but be prepared for her response one way or the other. If this is a 'here and now' relationship, go with the flow.
*hugs*
PS.. Have you found the larger apartment yet? It works for you with your financial affidavit, along with giving the kids more room. The limited size of your apartment could be used against you as inadequate.