The two daily Alfa-Pendular and three Intercidades trains leaving from Lisboa Entrecampos for the Algarve have Faro as their terminus.
To travel to Lagos by Train, one must descend at Tunes Junction and connect to a local train to Lagos.
If one searches the www.cp.pt in the panel on the top right hand of the first page for trains from Lisboa Entrecampos to Lagos and then click on the "details" link next to each result on the following page, it shows Tunes these details.
There are NO direct trains from Lisboa to Lagos.
However, we use the train regularly to get up and down from Lagos to Lisboa and the change at Tunes usually works like clockwork as one has +- 10 to 20 minutes to wait after the Lisbon train arrives before the Lagos one comes in and wanders of down to Lagos.
By public transport the only way to get from Lisboa to Lagos directly is by long-distance coach.
However, this takes a minimum of 3hrs:45mins with no stops! (On board toilet!) Not recommended for kids, especially in summer. (See: http://www.eva-bus.com/novo/)
There are slower buses www.renex.pt or www.rede-expessos.pt which do stop en-route for 15-20 minutes but these take up to 4hrs:30mins to do the trip.
Take it from an old hand....Take the train!