There is no direct bus or train from Lagos to Faro Airport.
You will have to get a bus or train to Faro and then another bus or taxi to the Airport.
As regards trains, the official CP timetable is clear. Year round there are two trains that operate daily that will meet your requirements:
Dept Lagos: Arr Faro:
06:11 07:51
08:19 10:03
There is also a departure at 09:46 arriving Faro at 11:27 which does not operate on Sundays or Public Holidays. Boxing Day is not a holiday in Portugal so it will probably run.
As regards buses, EVA Transportes has two buses that will meet your needs:
Lagos: 07:00 Faro: 09:00 Weekdays
Lagos: 08:30 Faro: 10:35 Daily year round.
From Faro Train/Bus Station you will either need to take a taxi or bus.
The following buses (16 or 14) run daily from in front of Faro Bus Station to the Airport:
0800, 0830, 0905, 1010, 1115,
