For info on trains between Lagos and Lisbon see the following sites:
www.solpraiaferias.com/index.php?content=cheg_en
Cubsur's www.algarvebus.info
www.cp.pt
Be aware that the train timetables wil change in September to a Winter schedule with a reduce frequency probably offering no more than 4 Lisbon services per day.
You take a local train from Lagos to Tunes - Change there to the expresses running from Faro to Lisbon Gare Oriente. For central Lisbon you probably want to detrain at Entrecampos Station.
When we visit Lisbon we either look for last minute deals on somewhere like lastminute.com or accomline or we stay at one of the IBIS Chain Hotels.
The IBIS Malhoa in Avenida Jose Malhoa is not bad as it is close to the Praça da Espanha Metro Station although you would have to take a cab to the Hotel from Entrecampos. They currently appear to have offers on that might fit you budget. Also have a look at the IBIS Barata Salgueira and IBIS Saldanha.
The centre is 10 minutes by metro/taxi from these hotels and they offer a combination of standard quality and economy.
Hope this helps
