Not had a chance to watch the videos yet, but my take is, and has been for a long time, that no, the US Lend-Lease Program didn't rescue the Soviets from defeat.
Lend-Lease did, however, make it possible for the Soviets to stop the Nazis sooner.
In August 1941 the Soviets began the wholesale evacuation of vital industrial infrastructure deep into the interior of the Soviet Union, kicking into full gear a program of moving critical assets and personnel East that started as early as 1940.
Many of those plants were back in production by mid-1942, well before significant quantities of Lend-Lease materials reached the Soviets. At the same time the Soviets were making incredible strides in building new production infrastructure from scratch. Lend-Lease did supply them with some vital components, such as tool steel and precision machinery, but perhaps the most significant deliveries to the Soviets weren't weapons, but food. The Nazi invasion overran much of the Soviet's grain producing areas. US pre-packaged rations could be supplied directly to the troops quickly and take pressure off transportation, allowing it to be used for other purposes.
The Soviets and later the Russians have always significantly downplayed the effects of Lend-Lease, while the west has always viewed it as having saved the Soviet Union from defeat and occupation.
The truth is somewhere in the middle.