I know it may seem mean to you to separate them, but it's best for the cats. It took my two quite a bit longer than two weeks to be able to be in each other's presence; hissing, growling and hiding are normal - the new one is invading the other's territory. They may hate the closed doors, but let them hate it; they will hate it more if a new cat-being is in THEIR territory and both will start to exhibit aggressive behavior because neither will feel safe. Let the new cat have a safe place, introduce them slowly - the towel swapping to get them used to each other's scents works extremely well.

Yes, it will be inconvenient for you for a while, but it's not forever. Your cats will (eventually) love you for it. Mishi was kept in my bathroom for his first several weeks with me. It meant I had to rearrange Mitzi's eating and litter box locations, but she was fine with that - she was the resident cat at the time, even though I'd only had her for two weeks before Mishi came on the scene. Now he and Mitzi cavort together throughout the apartment, but he still goes to the his bathroom when he wants to feel safe. It's taken them over three months to get to where they're almost sleeping together. They are getting closer and I will post a pic when it happens.

Good luck to you and your new Lily. Just remember to be patient and give them BOTH lots of loving; they're both scared and jealous right now.