best way fro faro to lagos

There is a train that takes you from Faro to Lagos.

https://www.portugaltrains.com/faro-to-lagos-train.html#:~:text=Faro%20to%20Lagos%20Trains&text=The%20whole%20journey%20takes%20anywhere,latest%20departure%20at%208%3A50p.

It may depend upon when you arrive in Faro and how many in your party. A private transfer could be more convenient and more affordable if shared. If you are going to use a car to explore the Algarve during your stay, a rental car makes sense, see if you need to return to Faro to leave at the end of your stay.