Unfortunately, Damas have renewed their website which is not exactly user friendly.
Have a look at their Algarvean counterpart EVA Transportes at this link:
http://www.eva-bus.com/lagos_sevilha.php?serv=lagos_sevilha
As from 16th October until 31st May, services will not run on week-ends or public holidays.
The 08:00 and 16:15 from Sevilla Plaza das Armas bus station will I understand still operate on weekdays.
There is also a daily service from Seville Plaza das Armas to Faro leaving at 15:00 Seville time arriving at 16:30 Portuguese time. This is operated by alsa.es
Currently there is an 18:14 train from Faro arriving Lagos at 19:56. You should check both timetables in a week of so to confirm winter schedules.
