While the allies did deliver a lot of goods to the Soviet Union through the lend-lease act -especially Studebaker trucks came in handy- , I don’t think this was crucial enough to make the Soviets lose Stalingrad if this help hadn’t been forthcoming.
The Soviets had managed to dismantle their factories in the months after the German attack on the Soviet-Union and had managed to replace them behind the Urals, safe from any German bombers. Some sources claim about 50,000 factories (from the largest to the smallest) were moved east.
They were totally outproducing the Germans when it came to tanks for example.
On the flanks of the German sixth army they had massed giant armies. Opposing these pincer movements were poorly equipped Italians and Romanians.
The Germans were unaware that the Soviets had so much strength left and thought they were finally dealing their enemy a knock-out blow.
Operation Uranus (the Soviet counter-attack) caught them by surprise, smashed in their fanks and completely cut off the German sixth army and supporting elements in the ‘Kessel’ or ‘Cauldron’ of Stalingrad.
At this point in the war the Germans were not under any dangerous pressure from the allies. The bombing campaign against Germany was not at its peak. No allied troops had been able to land in Europe, and the German Afrikakorps was tiny in comparison to the troops that were engaged fighting the Soviets.
It’s unlikely that the Germans would have been able to capture AND keep Stalingrad if the other allies had done even less to support the Soviets.