There are no direct public transport links between Lagos and Fatima.
By train it is not that easy as you have to transit Lisbon and disembark at Caxarias, 10km (6 miles) outside Fátima. There are only a few buses a day between Caxarias and the Sanctuary.
The best bet is by long distance coach.
I have published the current (Sept 2010) timetable for bus services between Lagos and Fatima via Lisbon Sete Rios Bus Station offered by Rede Expressos here:
http://scr.bi/94Pjqg
The word "Diariamente" means daily. The first two services of the day do not operate daily. I would suggest that to do the return trip in a day would be uncomfortable. You probably want to plan on staying over in Fatima at least one night.
The full site for the bus company is here:
http://www.rede-expressos.pt
