the problem with saying you "lost" it, and getting a new one with a more female picture on it is this: if you use the "old" one with the male picture on it when you present as male, if you get pulled over, all they do is slide your license, and yes, it will be coded that it is a lost license. You probably won't get in trouble, but the officer will ask why you're using what is not basically an expired license. Of course, that is against the law, so who knows what the officer will do. He may just ask where your new license is..... he may just take the old one.... or he may fine you / ticket you for using an outdated license.
An ID card would probably work best.... if anyone at the door of a club asks why you don't have a DL, just tell them you're epileptic, and cannot drive. (I've seen people give others a hard time for an ID card, and this excuse works wonders).
Keep yourself legal. You don't want to add legal problems just trying to figure out how to get a different picture.
Also, if you only need a new picture, and you do decide to change your license, you can just go in and say that law enforcement told you that you need an updated picture on your license. A lot of states, since it is all digital now, just print up the new license with the old pic that is on file... and you won't have a choice for a new pic. But using law enforcement as an excuse works great.