Haven't tried it, Pat, but I think you'd need to get a taxi from the airport to the station as the bus that goes to Faro via the airport is just an ordinary service bus and not really equipped to carry as much luggage as passengers, if you get my meaning.
We would have no problem at the Lagos end as our hotel is less than 300yds. from the station.
There again, however, a door-to-door taxi service is a nice,relaxing start and end to the holiday.