Actually there is a very good train service between Lisbon to Lagos.
Go to my blog:
http://barlaventostravelblog.blogspot.com/
Scroll down on the right until you come the panel entitled:
>>Algarve & Portugal - Travel Transport Links
Scroll down till you come to the item:
# Portuguese Railways - Winter 2007/2008 - Lisbon - Algarve Faro/Lagos Timetable
Here you will be able to download the timetable in pdf format.
The timetables may change in the next few weeks with the introduction of the summer 2008 timetable.
You can find the main rail site at:
http://www.cp.pt
The only way to get from Faro Airport to Lagos without a car is by taxi or private transfer.
See:
http://www.low-cost-transfers.com/
Hope this clarifies matter.
