You're an adult, OP, not a teenager, so don't do any of the petty shit advised here.
Take screen caps of the entire conversation and the dick pic and send them to yourself. Keep that as a record of what happened. Once you're clear of the relationship, delete it. You want to screen cap it so she can't delete it and make excuses.
When she gets home, have an adult, non-passive-aggressive conversation about it. Tell her the truth about how you found the texts, ask her what it's all about, and tell her that it violates your trust, and you aren't comfortable continuing the relationship.
You guys are on the lease together, so that's messy, but how long is your lease? If it's ending soon, perhaps you can ride out the lease together, then one of you doesn't renew it. I know you were wronged, but if you want to break as cleanly as possible, do whatever's easier. If she agrees to move, good. If she doesn't agree to move, you move, and then never speak to her again. Do that either way. The point is that you don't want to drag this out more than necessary. Another option is maybe talking to the landlord and explaining the situation, and maybe the lease agreement can be amended in whatever way you guys choose.
I know the bros want to tell you that she should be the one to move, fuck her, etc etc, but in my age, I think it's best to try and resolve it as smoothly as possible so you can get to the "moving on and putting her in the past" part quickly. You moving out doesn't mean she "won," or got over on you somehow. Her moving out doesn't mean you "won." You're adults. You just want to get out of this relationship as cleanly as possible. Good luck!