Ok, it’s not a day trip in the typical sense of the term, but since you have to go a little out of your way in Lisbon, and you can spend the better part of a day, I am calling it a day trip to Belem.
How to start trip to Belem

You can take Tram 15 from anywhere along the route.We went a slightly different way since our hotel was near a metro station. For €1.50 we took the metro to Cais do Sodré. Then for €1.35 we took the local Cascais train three stops to Belém.
The entire journey took us about 45 minutes. That’s a reason I call this a day trip.
After we exited, we continued in the direction of the train into the Garden of Afonso de Albuquerque and Garden of Belém.

Look around. You may find some hidden gems, as we found this Thai temple celebrating 500 years of good Thai-Portuguese relations.

Monastery of Jerónimos
At the other end we saw dozens of tour buses and we knew we must be near the Monastery of Jerónimos. We continued past the buses and into Praca do Império.

and got a view of the monastery.
Entrance to the monastery is €10. On the right you can get into the church for free.

You can even see Vasco de Gama’s tomb.

If you want, the Archaeological Museum is right next door.

Belém waterfront
We headed toward the water back through Praca do Império and through a tunnel under the railroad tracks to see the Monument to the Discoveries, celebrating 500 years of Portuguese exploration.

We then continued along the waterfront promenade past the Belém lighthouse.

We continued to our final destination, Belem Tower.

Cost is €6.00 to enter.
If you are lucky to be there at the right time, you may get to see the changing of the guard at the Combatants Museum on the other side of Belém Tower.

I don’t know what times that occurs, but I happened to be there at 12:15.
After that, feel free to wander through Belém and even get something to eat. It felt like a very clean, safe neighborhood. Pastéis de Belém, a block away from the monastery, seems to be recommended by everyone. But there was a huge line outside when we passed by so we moved along.
Summary: Trip to Belem
A trip to the Belem district is a must do if you are visiting Lisbon. I enjoyed this area, and Sintra, better than Lisbon itself.
The highlights of Belem are the Monastery of Jerónimos and the Belem Tower.