If he found things to amuse himself with in Barcelona, he'll be able to in Lisbon although as Trills pointed out it is a bit smaller. That said, if he's one of those teenagers determined not to enjoy himself on a family holiday with museums, he'll find it very easy to not enjoy himself.
The Estádio da Luz (Stadium of Light - Benfica stadium) does tours and is reachable on the metro system (Colégio Militar/Luz stop). Same for the José Alvalade stadium (home of Sporting Lisbon and its museum - at Campo Grande metro station). Both stadiums are next to giant shopping malls if that helps.
If he's into food try the TimeOut food market at Mercado da Ribeira (opposite Cais do Sodré rail station near the river). If he's the arty-farty type the bookstores and art shops in the Chiado area are worth wondering around - combine it with a visit to the Café A Brasileira and a ride in the Eiffel-designed Santa Justa lift. For more atmosphere, try walking up to the castle and then down through the Alfama district (or vice versa) and, at night, the bars/restaurants in Bairro Alto.
Unfortunately Lisbon's harder-core club scene is virtually non-existent although it is the home of fado music.
For beaches he'll need to take a train to Cascais.
One thing worth mentioning - in Portugal, cannabis (usually referred to as hashish) is as good as legalised and is pushed on the streets of Lisbon pretty openly. If he looks any older than about 14 he will be targeted. Lisbon is generally a safe city and I was allowed to wonder the streets at night by myself at that age when dinosaurs roamed the Earth but I'd probably think twice about it now if my teen was remotely interested in hash.
Drinking age is 18. It used to be non-existent, then 16, now 18 although enforcement is a little patchy.