Book online in advance is normally the best deal (no matter where you are going.)
In Europe I find that the best deals are always to be had using aggregators like Auto Europe, Holiday Autos, Argus Car Hire etc. rather than directly with the car hire companies Avis, Hertz etc. (No matter which channel you book through the actual car will come from one of the big rental companies)
(By contrast in the US you can often get as good or better deals booking directly with the hire companies in my experience)
All the major car hire companies will be represented at Lisbon Airport.