Well done for wanting to see more of Portugal!
Lagos and the Algarve, although lovely, are not Portugal. In fact, in the days of the Portuguese Monarchy, the Kings held the title of "Reis do Portugal e dos Algarve".
As kristalLisboa says, there are great places along the coast between Lisbon and Porto and even north of Porto. However, do not forget also that there are great places inland worth visiting such as the Serra de Estrela Mountain range, the University city of Coimbra, (combine with Figueira da Foz), and the Douro Valley.
Don't know where you are in Scotland, but Easyjet.com do now operate Edinburgh to Lisbon!
