During the original trilogy, there was an existing republic taken over by an empire, which also happened with Ancient Rome - was this a deliberate parallel?
Probably, but no one seems to have said so directly.
You are not the only one to notice the similarities.
For example, historian Tony Keen says this about it:
...the architecture on the planet Naboo resembles that of imperial Rome, and the pod race in “The Phantom Menace” rivals that of the Roman chariot race seen on screen in “Ben-Hur.” The transition from the democratic Galactic Republic to the dictatorial Galactic Empire over the course of the franchise also mirrors that of ancient Rome. “It is plain that the basic structure of Lucas’s history derives from the fall of the Roman Republic and the subsequent establishment of a monarchy...
Wikipedia also makes this claim (emphasis mine):
Star Wars, the space opera saga and cultural touchstone, is acknowledged to have been inspired by many sources. These include Hinduism, Qigong, Greek philosophy, Greek mythology, Roman history, Roman mythology, parts of the Abrahamic religions, Confucianism, Shintō, and Taoism, and countless cinematic precursors.
However, this claim seems to have been made solely based on Lucas saying
I love history, so while the psychological basis of Star Wars is mythological, the political and social bases are historical
and I can find no relevant quote directly related to Roman history.