We have a 4 hour priviate Tuk Tuk tour. It will take us whereever we want to go, but their suggetions: Lisbon Catherdral, Miradouro da Senhora do Monte, Feira da Ladra (flea market), Pink Street, Sao Pedro de Alcantara veiw point (but I think we can do that from the Castle), Pasteis de Belem (custard tarts???), and then Belem and Monument to the Discoveries. Since it is a priviate tour, we can add/delete and stay as long as we wish at these areas. Then once he drops us off at the Castle, we were planning on seeing the
Miradouro das Portas do Sol for the view, then head down towards the main square in the city centre (Praça do Comércio). Walk to the edge of the river where there’s a quay. (Two marble columns on either side of some steps lead into the water ?) Take a drink / snack break at the Terrace Ministerium.
Then head back up to the Santa Justa Lift to CARMO Convent and ARCHAEOLOGICAL MUSEUM. I do have notes as how to get there bypassing the lift if it is crowded. We would probably grab dinner there and then head back down to our hotel.
Does this seem doable to you?