cheylmcl: That first option from annemariet will not take that long (7 hours), but about 5 hours.
This is the best combination, for me:
Because if they take the fastest train (Alfa) in Lisbon, they will be in Lagos about 3h42 later on. There's an Alfa train departing every working day from Oriente's train station in Lisbon at 8h24 AM and the journey to Tunes will take about 2h40m. Then in Tunes they only need to change from the Alfa to the regional train, departing in Tunes at 11h07AM and this one will arrive in Lagos at 12h06 (hence the 3h42 minutes journey).
Then they need to take the bus in Lagos to Sagres, there's plenty of them all days, and there's one departing at 12h40 arriving in Sagres at 13h35. Now, Lagos' train station is just near the marina. This is piece of cake. The Bus terminal is in the other side of the marina, so they will need... er... to swim a lot... near sharks...
no, not really. :) There's a small bridge connecting both sides, and the Bus terminal is just around the corner, first road to the right side after the bridge. Easy! They just will need to wait about 35 minutes... enough time to buy an ice cream or take some photos. lol
So if they catch a train in Lisbon at 8h24m, they will be in Sagres at 13h35. 5 hours. 25€ the Alfa-Regional ticket in 2nd class.
This is the only Alfa train from Lisbon in the morning. There's another in the afternoon departing at 18h24.
Between each one there's the Intercities train (10h20, 14h20, 17h20) but this one will take a little longer.
If you want any more help, ask.