Do you do a lot of sport as a translation sounds weird in English..

You don't "do sport," you "play sports," in American English, at least. And we would use much as an adverb for play, rather than use an adjective modifying sport. Maybe other English-speaking countries would differ, though.

Bă tzigi e greşit pă engleză

Do you do sport a lot = same thing

Bad English

Although the English translation sounds awkward to native English speakers, it should be kept because it shows the literal meaning of the words.