Osimhen opened the scoring after 16 minutes when he converted a penalty after Sassuolo’s Daniel Boloca brought down Matteo Politano.
Maxime Lopez made things worse for the visiting team when he was sent off in the 51st minute for verbally abusing the referee.
Napoli were awarded another penalty around the hour mark when Jeremy Toljan handled the ball, yet Giacomo Raspadori’s effort sailed over the bar.
Khvicha Kvaratskhelia’s perfectly timed through ball in the 64th minute sent Di Lorenzo on a clear path to score as he doubled Napoli’s lead.
Lazio’s Serie A struggles continued as Genoa secured the only goal through Mateo Retegui’s header from a rebound in the 16th minute. Lazio have now lost both of their Serie A matches this season.
(Reporting by Tommy Lund in Gdansk)