There is a bus operated by Renex (www.renex.pt) that leaves Lisbon Gare Oriente bus station (10 minutes by taxi from the Airport) at 01:00 and arrives in Faro at 05:15.
Please note that this service operates every day except on Saturday to Sunday night.
From Lisbon Sete Rios Bus Station there is a daily service operated by Rede Expressos as follows:
Dept: 01:00
Arr Faro: 04:50