First of all you do not want to head to Faro!!!1
Take the train from Lisbon to Tunes junction and then change to a train to Lagos.
Go to my blog here:
http://barlaventostravelblog.blogspot.com
In the right hand panel half way down you will find a section entitled:
Algarve & Portugal - Travel Transport Links
You will find links to the necessary train timetables there.
In Lagos walk over the Marina bridge to the Bus Station.
From Lagos there are regular buses operated by Eva Transportes from Lagos to Sagres:
Timetable here: http://bit.ly/6CpGiy
