The US Army's official history of World War II, called the Green books, has an entire volume that deals with Aid to Russia The Persian Corridor and Aid to Russia http://www.history.army.mil/html/books/008/8-1/index.html

Reading that volume you can get a full understand of WHAT was supplied and how.

Clearly there is some bias given when it was written, 1952, and the group that wrote it. In part the books were written for future military planners so it is clearly not a PR piece. Having read with an economic background and logistics geek it is a great single source on the topic.

It is hard to assess this question accurately, because when we place the Lend-Lease scheme in the context of the Cold War, it becomes a weapon in any post-war propaganda duel. Indeed, until Nikita Khrushchev, any archive material on the Lend-Lease scheme was off limits, and even with some relaxations in policy in Russia under his premiership, anything claiming that Anglo-American aid had any significance were unacceptable. While Western historians obviously had free reign on their opinions, access to archives could be considered critical in this debate. Why? Well, despite no paucity of academic (and political interest) in the subject after the war, a lack of information on where the aircraft/tanks/resources were going, as well as on Soviet production and losses, renders a balanced assessment almost unattainable. Even with the opening of the archives (and some material remains classified), many Western historians continue to maintain that aid only became significant in 1943, after the Soviets had gone on the offensive. However, the key part of the Lend-Lease scheme lies in aid supplied between 1941/42.

Just going to go through some stuff which is fairly conducive to the rest of the answer. There was a lot of (primarily Republican) opposition to the idea of the Soviets receiving aid on a Lend-Lease scheme. Nonetheless, after the Nazi invasion and initial Soviet approaches to the US, the US unfroze Soviet assets worth around $40,000,000 (likely a legacy from the Tsarist era) and ignored the provisions of the Neutrality Act of November 1939, obstructing arms sales to the Soviets.

However, the Soviets needed to be allowed into the Lend-Lease scheme (they were still paying for arms at this point) in order to receive much benefit from the US, as they had very limited foreign currency reserves. It was slightly more difficult than expected to include the Soviets into the plan, due to the British dependence on the US for a lot of supplies (1), and there were concerns about the US ability to supply both Britain and Russia. However, despite these concerns, the British and US were willing to supply 400 aircraft and 500 tanks a month (this would require significant increases in US output). The US made commitments to supply 1.5 million tons of supplies during the First Moscow Protocol, which went up to the 30th June 1942. The Soviets were to pay, by cash advances on deliveries and future raw material supplies. On the 7 November 1941, Roosevelt finally incorporated the USSR into the Lend-Lease act.

Basically, the system was set proportionally, so the US would supply a certain proportion, and Britain would fill the rest. When the US share fell as the war with Japan began, the British were able to account for the difference. The question at hand is the delivered item’s significance, and it seems British supplies were of some importance, as while over the whole war British supplies pale into insignificance, they were some 10% from June 1941 to June 1942 (of tanks - the British supplied around 1,500, the Soviets produced around 15,000). While the British tanks supplied were mainly Matildas and Valentines (many of which were produced in Canada), which were certainly inferior to T-34s and KV-1s, these tanks were only beginning to become ‘seriously produced’ in the USSR in 1942. There were other problems with the Matildas and Valentines. Their 40mm turret was found lacking, and they were not suited for Soviet conditions (some pneumatic parts had to be replaced, and the British replacement parts were not up to scratch) among other things. But the Soviets were facing high tank losses. According to one statistician, the Soviets lost 20,000 tanks between June and December 1942. As such, the Soviets were obviously keen to press as many tanks into service as possible.

Now, I could go on for hours about various tank strengths, and their proportions of the Soviet whole, the important thing to note is the British figure (as a proportion of the Soviet whole) does remain fairly constant at 10%. Aircraft too were important - 15% of the planes defending Moscow were Tomahawks and Hurricanes, for instance. While we have to place this whole debate in the context of the Cold War, the very reason these supplies were requested was because the Soviets needed them. Whether the Soviets could have sustained 5-10% less of its fighting strength (2) is a question that is very hard to answer. To me, the debate hinges on this point. Of course, supplies increased massively into 1943, but this is largely irrelevant to the question at hand. There may be some revelations in the future, as some documents on the use of Anglo-American supplies are still classified.

One assessment I've seen is in Hubert P. Van Der Tuyll's Feeding the Bear, which despite being written before the opening of the archives, suggests that the aid allowed Russia to fight an offensive war, rather than a defensive one. That would suggest that yes, it changed the course the war by shortening it significantly, although his facts are sometimes slightly odd.

(1)See the destroyers for bases agreement for one example.

(2) I’m going to summarise with this figure, because otherwise this is going to turn into a Journal article - there are a million things to consider, radio quality etc. and I haven’t fully considered tanks or planes, or even looked at supplied ships/submarines during 1941/42.

EDIT: Added a paragraph on Feeding the Bear.

It was certainly a major help, but the Soviets deserve most of the credit for winning the European theatre ground game. US/British/Canadian/Austrailian air and sea power were probably more important to that part of the war than anything else - the Luftwaffe and German Navy were basically gone by the last couple of years.

You might want to clarify what you mean by Western support. Do you mean Western support as a whole, including the idea of a second front and the allied bombing raids, as well as the lend-lease scheme's support to Russia? Or do you just mean the lend-lease scheme (which I think is implied in the question)?