You can get down from Lisbon by either long distance bus or train.
Cost will be between € 16:00 and € 23:00 per person each way dependent on which service you chose.
Buses:
Eva Transportes/Rede Expressos operate several daily services leaving Lisbon Sete Rios Bus Station / Metro Jardim Zoologico Bus Station and taking approx 3hrs45min to Lagos.
Renex operate several daily services from Lisbon Gare Oriente Bus Station to Lagos. Transit time circa 4hrs30mins.
Trains
Take between 4hrs and 4hrs:30mins. Note you have to changre trains at Tunes Junction and take an Algarve Line train to Lagos.
If you visit my blog:
http://barlaventostravelblog.blogspot.com/
»» Scroll down on the right hand side until you come to the panel entitled "Algarve & Portugal - Travel Transport Links"
»» Click on:
- Porto - Lisbon - Faro Train Timetable
- Algarve Regional Line Train Timetable for connections along the Algarve.
- RENEX Bus Service - Lisbon to Algarve timetable
- Rede-Expressos - National Bus Timetable - Updated. (National Coach Operator) - Portuguese only.
- Eva Bus Service - Lisbon Sete Rios to Lagos
Also see Cubsur's excellent site here, complete with the Lisbon to Lagos Timetable.
http://thomasallen.home.sapo.pt/travel/006.htm#times
Bus is cheaper but train is more scenic and at least you can walk around.