Firstly, be aware that there are ongoing periodic strikes/work to rules affecting Portuguese Railways. You should check status 48 and 24 hours before prior to travelling at the Railway's website:
You can find the timetable for the line (Linha do Sul) here:
If your final destination is really Faro there is a good chance that there will be minimal problems. Both Intercidades and high speed Alfa-Pendular services operate between Lisbon Gare Oriente Station and Faro and are only minimally affected by work-to-rules.
In the unhappy event you get hassled by strikes you can always take a long distance coach from Lisbon to Faro.
www.renex.pt operates buses from Lisbon Gare Oriente Rail/Bus Station to Faro. Again take the Metro three stops from the Airport as indicated above.
www.rede-expressos.pt operate in excess of 12 services daily from Lisbon Sete Rios Bus Station to Faro.
To travel from the Airport to Lisbon Sete-Rios/Metro Jardim Zoologico take the Aerobus Line 2 Bus from outside the main arrivals hall at the Airport. The service runs every 30 minutes from 07:30 to 22.00. Takes about 25 minutes depending on traffic.
Finally, bear in mind that TAP-Air Portugal operate 3 to 4 daily feeder flights from Lisbon to Faro Airport.
