There is no easy train connection as Fatima station is 20km from Fatima with infrequent bus connections.
There is effectively only two ways to currently make the trip:
By Road:
Viamichelin.pt gives a distance of 381km one way with a transit time of 4hrs 15minutes, so +- 800km return trip by toll motorway.
Based on February 2015 prices, the estimated cost by car would be:
Tolls: One way 31.35 €
Fuel (based on prevailing prices): 43.62 €
By Bus:
By public transport, one would have to use the long distance EVA TRANSPORTES/REDE EXPRESSOS bus service via Lisbon Sete Rios Bus Station.
See the Rede Expressos website: http://www.rede-expressos.pt/
A day return trip only really works on weekdays. If one catches the 05:45 EVA departure (Monday to Friday) from Lagos Bus Station, one arrives in Fatima at 11:30. There is a 60 minute layover in Lisbon.
One can then get the 18:30 departure back from Fatima, arriving Lagos at 00:15. Again there is a layover in Lisbon.
These are both daily services and times are correct as of February 2015.
As far as the writer is aware, there are currently no organised day-trips from Lagos to Fatima.
One can contact the information services at the Sanctuary for more information about the Sanctuary: www.santuario-fatima.pt/portal/index.php
By Aracuano (Own work) [GFDL or CC BY-SA 3.0], via Wikimedia Commons