There are some affordable hotels close to Lisbon Airport, but for most visitors it’s best to pay a little more and book a place in the city center.
Hotels in Lisbon tend to stay busy most of the year, but the official high season lasts from June through September. Since this isn’t a beach city it doesn’t get overloaded during July and August the way the Mediterranean cities do, but still if you are coming during summer it’s best to book ahead.
During most of the rest of the year it’s usually quite easy to find a hotel room once you arrive, although the Christmas holiday season is popular everywhere so if you are coming then you should definitely book as far in advance as possible.
Several hostels in Lisbon continue to get excellent marks from past guests, so even if you aren’t traditionally a hostel person it might be worth looking into here, especially since all of them have private rooms to go along with their dorms.