At MEPS I lied about something. What happens if I bring it up?

Let me preface my response with this: I understand very well how personally important military service can be for people... it was for me. I even understand how tempting it is to do just about ANYTHING to get it. I get it. I really do.
But as much as I sympathize with your situation I have to say that lying at a MEPS interview is probably one of the dumbest things you could have done.
Had you been truthful in your interview they may or may not have accepted your application -- they might have allowed a waiver or allowed you entry for a combat service support MOS -- they have a lot of scope for that sort of thing. But now that you have lied, the Army may chose to separate you for lying in your application. I doubt they would prosecute -- though what you did is illegal. But continuing in the lie -- especially one that will be discovered if you ever need to apply for a security clearance -- is not something you want to do. You will eventually be found out and the longer you leave it the worse it will be for you.
The reason they ask you about things like depression is because in a warfighter environment you will (not may be, not could be, but WILL) come under tremendous stress.
Previous bouts of depression -- particularly where medication has been required as part of the treatment -- raises the spectre of a potential that you will not be able to cope when heavily stressed. De-compensating in a combat environment places you and those around you in unnecessary additional danger.
You were not asked that just because the doctor thought it was a cute question -- you were asked because they were trying to assess any risk you might pose. The fact that you lied about it -- and now seem to want to blame your recruiter for that lie -- calls into question your integrity and moral fiber as well.
This is not a question about what other people do or do not do. This is about you and your ownership of a wrongful act -- lying in your interview.
My advice to you is simple. Come clean now -- the sooner the better. Take your lumps and get on with your life. Who knows but maybe it will be okay. The army seems more warm and fuzzy now than it was when I joined back in the day. In any case, if you persist in the lie it is going to haunt you the whole time you serve. Every time a personnel action comes around you will be worrying if they're going to catch you.
Brother, that is no way to live.

I don't but the "like most people" comment, but the fact is that you have an issue. Own up to it, get the treatment for it you need, and get out in front of it. If you are honest now, accept therapy/treatment, who knows? My guess is if you are just out of boot, or before, you can be discharged for good of service. But, I strongly suggest you talk to a JAG. You aren't the first one, and certainly won't be the last. With the recruiting #'s as bad as they are, they may still keep you depending upon what the issue is...

Now, as an example... I once had a suicidal sailor that worked for me. He managed to pull a gun on me (he was going to take us both out), and I talked him down after 4 hours. He had issues that he was upfront about, got treatment, and he went on to serve for another 10 years. So, whatever issues you had can be overcome, but it will be up to you. If you want to stay in, work to get better, tell the truth, and let the chips fall where they may. You may find out that it is a lesser thing than you think it is. Talk to the lawyer. Talk to the mental health professional. You will only make it worse, IMO, if you keep denying, but that is a decision you have to make for yourself based on all the info you take in.

Best of luck to you!

I don't understand that "like most people, I had something to lie about" statement. I don't know of anyone I served with that knowingly lied. Tell the truth and take personal responsibility for your actions. That is what is required in the military, and it is what is required in life as well. If you make a mistake own up to that mistake. I respect and admire those who do.