Long sigh....
OP: No, do not lie on the medical form, most especially for anything which is documented in federal records. Most, most especially for something previously documented with the FAA. Federal prison time is at stake.
Good news... if you're off meds, and have recovered you can fly, just have to jump through a few hoops. Don't have to wait any abitrary time period if you've been well for a while, just have to do the paperwork and whatever evaluation they may want you to get.
Bad news... if you have a mental health diagnosis with the VA, that's a problem. Typically the advocates who help vets apply for VA benefits seek to maximize the disability rating, but that can backfire if you want to fly as a civilian if the condition is disqualifying. If the VA is giving you a percentage (other than zero as a placeholder), then you're probably going to need to get that diagnosis resolved before you go to the FAA. I'm pretty sure that you cannot have a rating for anxiety, depression, or most PTSD and then claim clean mental health for the FAA. Note that you can have ratings for things like bad knees, bad back, hearing loss, etc and many airline pilots do. Just not things which are disqualifying in and of themselves.