Lagos to Sintra.
You have two options:
1) Rail
Local train from Lagos to Tunes
Intercity from Tunes to Lisbon Entrecampos
Timetable can be downloaded from my blog here:
You can find a link to timetables on my blog here:
http://barlaventostravelblog.blogspot.com/
Scroll down on the right hand side panel till you come to:
»» Algarve & Portugal - Travel Transport Links
»» Continue scrolling down in this section till you come
Portuguese Railways - 2008 - Lisbon - Algarve Faro/Lagos Timetable
Suburban train from Entrecampos to Cacem - Weekdays trains every 20 minutes or so
Suburban train from Cacem to Sintra - Weekdays trains every 20 minutes or so.
2) Bus
EVA Bus from Lagos to Lisbon Sete Rios Bus Station.
You can find the timetable here on my blog here:
http://barlaventostravelblog.blogspot.com/2008/07/lagos-to-sintra-to-cadiz.html
Suburban train from Sete Rios to Cacem - Weekdays trains every 20 minutes or so
Suburban train from Sete Rios to Sintra - Weekdays trains every 20 minutes or so.
3) Sintra to Cadiz
Suburban train from Sintra to Sete Rios - Weekdays trains every 20 minutes or so
Suburban train from Cacem to Sete Rios - Weekdays trains every 20 minutes or so.
Long distance coach with www.alsa.es from Lisbon Sete Rios Coach station to Jerez la Frontera. (Current Timetable)
Dept: Lisbon: 09:00
Arr: Jerez la Frontera: 20:00
Dept: Jerez de La Frontera 21:35 (Train Renfe)
Arrive: Cadiz 22:24
Dept: Lisbon: 21:30
Arr: Jerez la Frontera: 08:30
Dept: Jerez de La Frontera 09:30 (Train Renfe)
Arrive: Cadiz 10:19