Early morning metro trains in Lisbon
I have just returned from Lisbon where we stayed in a hotel (the Sano Reno) near to the Sao Sebastiao metro station. There are a number of hotels in this area within walking distance of the station. Sao Sebastiao is the terminus of the line to the airport so no line changes are needed. At a guess, the journey time is about 20 to 25 minutes.
The first train departs the terminus station at 6:30 am, so it is an option if this allows you to check in on time. Otherwise taxis are better for you and hotels closer to the airport would be preferable.