New Zealand's Lawson races for Racing Bulls, which is Red Bull's sister team that is traditionally used to develop young drivers.
The 24-year-old finished seventh at the Dutch Grand Prix and sits ninth in the standings with 49 points while his Red Bull teammate Max Verstappen, who crashed out of his home race on the opening lap, is sixth.
"Liam will drive alongside Max at the Italian Grand Prix in Monza, while Isack continues to make encouraging progress following the wrist injury sustained during the summer break," Red Bull said in a statement.
"The team is closely monitoring his rehabilitation and will take no unnecessary risks with his return to competition and wishes him a speedy recovery."
As a result, former Red Bull driver Yuki Tsunoda will retain his seat at Racing Bulls alongside British-Swedish rookie Arvid Lindblad having come in as a replacement at Zandvoort.