Of the various Miradouros in Lisbon, Santa Luzia is probably my favorite.
Trying to get those spots free of people is completely futile. I’ve only been there at noon time, and I strongly suppose it won’t be different in the evening. Early morning could be an option, but then, this spot was too far from my hotel to make me try it.
Still, if you’re interested in a good spot for a sunrise over the river, the lower terrace east of the church would be a good place in winter and early spring. Even better would be the higher terrace of the café, but I guess it will be closed in the morning.
Btw, the mighty church with the two towers on the hill is the church of the monastery São Vicente de Fora. The other one with the cupola is Panteão Nacional, the National Pantheon. We’ll get to both in due time.