Hi Jim, my immediate reaction was not a chance but then thought about it and now its a maybe. The 1st day(night) out of Lisbon would start you off going through the Alfama district which is not a bad night time place to start, then you start eventually to go down to the river front and that is straight forward to the Parcoes Nacional after that it might get tricky because you have to head into the Moscavide area and find a way out taking you North West and being able to see the arrows which point off to alpriarte, this section might be easiest which eventually leads to Alventejo. Its the next section which you would start in the next evening that would test your patience there is a lot off National Highway Walking, its bad enough in the day, at night I feel it would be more dangerous. I will pm you and suggest an alternative for the 30km section before Azambuja, which is trail but on private land and with its own potential pitfalls, I started on a alternative route than the one from Lisbon and the Fatima pilgrims I met alerted me of this possible alternative way out of Lisbon. The next day out of Azambuja is straight forward if you are vigilant and have a good torch and know from studying the various maps the twists and turns that will eventually lead you to Santerem, the same goes for the section to Golega. After Golega it gets very tricky, from reading various posts on here and meeting a pilgrim who it happened to it is quite easy to get lost in the day in a large forested area on a section before Tomar, the same goes again for the section after Tomar to Alviazere and from there to Ansiao. Another thing to take into consideration is the complete lack of facilities on some stretches, and the ones that are there are unlikely to be open during the night.
Good Luck
Mike