Di Lorenzo, who had an earlier goal waved off by the VAR, bundled in from close range in the 73rd minute following a rebound of a header by Scott McTominay.
Antonio Conte's Napoli moved five points ahead of defending champions Inter Milan, who host rivals Juventus on Sunday.
Lecce remained one point above last-placed Venezia.
Di Lorenzo's goal came a minute after Khvicha Kvaratskhelia came on.
It was Napoli's fourth straight win. The 2023 champion haven't lost since dropping their season opener in August at Hellas Verona.
Napoli are not playing in Europe after finishing 10th in Serie A last season. Up next, Napoli visit AC Milan on Tuesday.
Milan's match at Bologna scheduled for Saturday was postponed due to heavy flooding in Bologna.
Atalanta moved up to fourth by scoring five goals in the first half of a 6-1 win over visiting Hellas Verona.
Mateo Retegui and Ademola Lookman scored twice and Atalanta captain Marten de Roon and Charles De Ketelaere also were on target.
Retegui boosted his league-leading tally to 10 goals in nine matches.
Amin Sarr pulled one back for Verona before the break.
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