In case you have forgotten your driving license, it is possible that you won’t be able to get a car rented from Lisbon Airport, but do have a word with the person at the car rental desk, some suppliers have solutions for such problems. For instance, they can get a copy of your driving license information online from DVLA; however, note that for this you would have to pay a fee.
In case you have lost your driving license, you can request a car rental but only if you have a police report at hand.