How can I prove that the father of my child lied to the judge?

I recently went through a custody battle; during which the father of our child produced a fraudulent lease agreement. The judge awarded 50–50 based on a living situation which is a lie. He claims to be renting a room in a friends house, when in reality I pick up/ drop off our daughter at a one room apartment with 4 adults, 3 children and 5 chihuahuas. I am worried sick about my daughter but don’t know what i can do. Any feedback is more than welcome!