ALisbon: Transportation to Lagos- when is the best time to make reservations?
You can book the train ticket whenever you want. On the day, at the train station, or online: https://www.cp.pt/passageiros/en/train-times
ALisbon: A week in Portugal- how many days should I plan to spend in each city?
There is a train from Lagos to Lisbon Lisbon. I would stay 1 day in Sintra, 2 days in Lisbon & the remaining days in Lagos.
ALagos: Do we need a car or would public transportation be better in Lagos?
To find the most amazing "unkown" beaches, you def. need a car! When I travel to Lagos, I normally take my car is i bring more than 2 people with me. There are many cool places to stay along the beach.
ALagos: Looking for a 4 star type hotel in a central location in Lagos, Portugal?
I would recommend Hotel Vila Galé Lagos V