Those hotels are not in the periphery as many would exaggeratedly think.
Lisbon is not only the ancient part of Alfama, Rossio, Baixa and Bairro Alto. It's larger - though not like Moscow or Greater London of course.
They're not in the central point considering the central point as Rossio Square, though Ritz is in the business part of Lisbon, close to a central metro station with 2 lines - Marquês de Pombal - and within walkable distance from Rossio across Avenida da Liberdade.
The most central part of Lisbon is Rossio indeed. But it's not the oldest (it's Alfama), nor it's the business part (that's to the north between Avenida da Liberdade and Campo Grande).
Lapa Palace if I am not wrong is in a posh district to the west called Lapa (means limpet), which is also quite old and hilly area that resembles Alfama. The difference is that it's an upmarket neighbouhood. You probably won't notice that. It simply became a fad once for some rich chaps to buy and renovate old houses there.
It's located more or less between Estrela, Alcântara and the parliament.
There's no metro to there, and driving in twisting narrow streets may not be the best. Tram 28 passes nearby as well as some other old tram lines.
I see that you're looking for upmarket hotels. Lapa is classy in an old district, while Ritz is a modern building in a not so old area. The choice is yours.