Episode 40 of "House"
s02e18 Sleeping Dogs Lie

A young woman, Hannah, hasn't been able to sleep for 10 days. She's brought in after she downed an entire bottle of sleeping pills and still didn't fall asleep. Meanwhile, Cameron accuses Foreman of stealing a medical journal article she wrote... he denies stealing it, insisting he wrote his own article about the same case and it was printed before hers was submitted. As Hannah's condition deteriorates, it becomes apparent that she will need a liver transplant to give House enough time to try to solve her case. Her girlfriend and partner, Max, is a perfect match and agrees to donate part of her liver, despite its being a very dangerous procedure. However, the team discovers vital information about Hannah and Max's relationship, forcing them into an ethical quandary that potentially eliminates Hannah's chance of survival.