Donyell Malen struck twice inside the opening 23 minutes, either side of a third from Matías Soulé, before Rodrigo Mora added a fourth in the second half to complete the rout at the Via del Mare.
AS Roma have now scored eight goals without reply in their first two matches of the season, following an identical 4-0 win over Fiorentina on the opening weekend.
Head coach Gian Piero Gasperini was pleased with how his side handled another difficult away trip.
"We'd already had good experiences like this last year, even in very tough stadiums. This team is gaining more and more confidence in its qualities and more personality," he told DAZN.
"Dybala's fitness is clearly a boost, because the rest of the group — Soulé, the midfielders, the defenders — have always been there. Now up front we have a cutting edge too."
Asked whether Malen, who has now scored five goals in Roma's first two matches, was the best forward he had ever coached, Gasperini was effusive but measured.
"I've been lucky enough to coach plenty of strong forwards — going back to Milito at Genoa, and at Atalanta I always had strikers who were either top scorers or very close to it," he said. "He has this ability to control, shoot and accelerate over a few metres that just burns you. We made a good bet on him, and it's paying off."
On Roma's title credentials, Gasperini was cautious about drawing early conclusions.
"I've always said Inter have a head start on everyone. Then there are teams building themselves up impressively — Como certainly isn't a surprise package any more, they're a side of real quality. And then there are the big clubs: Napoli, Juventus, Milan. We have to focus on our own path," he said.
For Lecce, head coach Eusebio Di Francesco was left to pick up the pieces of a heavy defeat.
"We'd prepared the match differently and the early goal changed our plans, but they overwhelmed us in every department, and the responsibility is mine alone. We came apart at the seams — we'd prepared for certain situations and got none of them right. We were up against a great side that impressed me," he told Sky Sport.
Di Francesco was particularly frustrated by his side's flat performance after a promising start to the season.
"This match can be misleading — we were dreadful and they were excellent. We have some unusual situations in the squad related to the transfer window, like Tiago Gabriel, who I didn't see with his usual presence today," he said, before addressing his team's response to going behind. "I've faced difficult moments before in my career, but today it was too easy for them, and we need to work on our character. I saw this squad differently during the week — we have to react immediately."