I will move to California in January and I really need to take my cat with me. I will fly from Lisbon to Newark and then San Francisco with United Airlines. I know that they accept animals as cargo and also in the cabin. However this last bit of information is not very clear for transatlantic flights. I called United and It was confirmed to me that they fly with small animals in the cabin. But I also read some comments saying the opposite. Did anyone try to fly with a cat/ small dog in a transatlantic flight recently?
United's rules for in-cabin pets are clearly described on their website.
In short, yes, you can travel with your cat in the cabin, however it must remain in a carrier underneath the seat in front of you for the entire trip. There is a $125 fee per one-way trip.
Alternatively you can send it as cargo, which will cost more but may be more comfortable for the animal as you can use a larger carrier.
Your two flights are about 9 hours and 7 hours long (from boarding to unboarding).
Before the merger, United airlines did allow in-cabin pets on trans-atlantic flights, but Continental did not. I don't know the post-merger situation.
The only way to be certain is to call the airline and ask. You will have to pay a fee (probably around $100) to reserve a spot for your pet in the cabin (there is a limit on the total number of in-cabin pets carried on the flight). If they allow you to make this reservation and pay the fee, then you can be reasonably certain that they'll let you take your cat onboard. (-:
Note that if your total itinerary is operated by multiple carriers, you will have to call each operating carrier separately.