The Renex buses from Lagos to Lisbon Gare Oriente go through Alvor.
To make the 11.25 at Lisbon airport you would need to get the 00:45 service arriving Lisbon Oriente at 05:00 as the early morning service does not go through Alvor. Cost will be +- Euros 15:00
You could get the early morning train but you would need to get a taxi to Portimão-
For Renex & rail timetables go to my blog at:
http://barlaventostravelblog.blogspot.com/
Scroll down on the right till you come to the panel entitled:
Algarve & Portugal - Travel Transport Links
Click on
RENEX Bus Service - Lisbon to Algarve timetable
to download the RENEX Timetable
and
↓ Portuguese Railways - Summer 2007 - Lisbon - Algarve Faro/Lagos Timetable
to download the Railway Timetable.
From Gare Oriente take a taxi to Lisbon Airport - 5 minutes.