The league leader won the Serie A 1-0 victory on Saturday and won the championship with a 1-0 victory on Saturday, which kept visitors away from Scudetto rival Inter Milan.
Naples rose to 77 points, Inter's 74 points after defeating Hellas Verona late Saturday. Lecce ranks 17th in the ranking of the relegation zone.
Giacomo Raspadori's free kick in the first half was enough to win Napoli's highest three-pointer and fourth victory, while Lecce played 12 games without a win.
"It's an important step, I can't lie," said Naples coach Antonio Conte. "We're on the right track and we want to stay there until the end.
"No one will remember if we finished second, or if we had a good season. Having to write history and you win: Others read it."
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Emotion and anger are through Del Mare in the air in the stadium, which has nothing to do with Lecce's unstable league position or the fact that they have failed to win home games since December.
The game was preceded by a minute of silence in honor of recently passed away LECCE physiotherapist Graziano Fiorita, who both groups gathered near the family seats.
The death occurred as LECCE prepares for the final match against Atalanta and then rescheduled from Friday to Sunday, but Lecce is upset that he was forced to play shortly after the bereavement.
Lecce fought Atalanta without a logo, with the word "value, no color" on her chest, and towards Naples, fans turned to show anger.
The opening time came after the fireworks and flares fell behind LECCE goals, and the game was interrupted for five minutes when some of them landed on the court.
Before the shutdown, Napoli found the net in the second minute, but Romelu Lukaku's goal was ruled out in offside.
After the game resumed, Napoli did lead in the 24th minute, with Raspadori taking a low free kick from the edge of the box to the distance.
Lecce approached when Kialonda Gaspar rattled from one corner and Raspadori had a chance to double the lead but was fired after being sent by Scott McTominay.
Napoli was not allowed to score earlier in the second half before McTominay clearly pushed the goalkeeper to a header by MathÃas Olivera, but after that, Lecce had a hard time finding the equalizer.
Thorir Helgason's Dipping shot was tilted by Napoli goalkeeper Alex Meret, who fought for Meret before the ball was upright.
Naples pulled everyone back to being late and contented with a narrow victory, and the remaining three games solidified Conte's side.
Information from Reuters and the Associated Press is used in this report.