In other words, how significant was American lend-lease in helping the Soviet front? Would the Soviets be suffering a lot more had lend-lease not happen, or was it not as significant as people make out?
As others have pointed out, it will never be possible to answer this question conclusively based on documents, because the Soviet officials have always been eager to downplay (for the propaganda reasons) the importance of the Allied contribution to the war in general and Lend-Lease in particular, so all the official Soviet sources are suspect (as, by the nature of the USSR, they cannot be independently verified).
The only way to evaluate the impact of L-L is based on circumstantial evidence.
The bottom line is that, yes, "Soviet troops got into Berlin riding American trucks, walking in American boots and using American trains", but they also flew both American and Soviet aircraft, rode mostly Soviet tanks, fired Soviet rifles and canons (with US gunpowder) &c &c &c. Without the Western Allies, both their military action and Lend-Lease, the SU would have certainly not been in Berlin in 1945, and might not even been there in 1946, if ever.
This is a very hard question to answer for numerous reasons and one that will never be answered to everyone's satisfaction. Here are some things to consider and some problems that frequently come up when you're dealing with Lend Lease.
First off, significant Lend Lease aid was not felt until 1943. The Lend Lease that arrived before was nowhere near enough to make a decisive difference on how 1941 and 1942 turned out. There are some articles/arguments that have recently come out which attempt to argue that the Lend Lease tanks that did make it in 1941 played a decisive role in the defense of Moscow, but I don't believe they are conclusive enough (see the following article: British “Lend-Lease” Tanks and the Battle for Moscow, November–December 1941—A Research Note).
Secondly, the immediate problems that come up when attempting to qualify Lend Lease are the following. Just quoting numbers of what was sent is not enough. One needs to account for what was sent, when it arrived (and how much arrived), and when it was actually incorporated into the Red Army and used in the field. Additionally, one has to keep in mind that the Soviets began to scale back production of certain things because they knew they would receive them through Lend Lease. One example is trucks. The Soviets were producing practically none because they knew to expect them through Lend Lease, but that doesn't mean they couldn't produce more if they needed to. Many former truck producing factories were switched over to light tank production. Since the Red Army moved to relying on medium and heavy tanks, light tanks were something the Red Army could in theory do without or with less of. This type of analysis needs to be applied to everything the Soviet Union received. Specifically, what they received, if it was not coming through Lend Lease what were the alternatives? Meaning could they produce it internally or import it from another state/country (England, Canada, etc.). The Soviet Union did not just receive Lend Lease from the US.
Finally, the Soviet Union participated in reverse Lend Lease, sending back materials to the US. All of the above is just the tip of the huge iceberg that studying Lend Lease means, it's simply impossible to account for all the variables.
Firstly let's talk about the total aide that Russia was provided with through the Lend/Lease Act. It appears as though by 1946, the United States had lent about $51 billion in total with $11 billion going to aide the Soviet Union. That's a substantial proportion. Almost 25% of American aide going to the Soviets.
But with the total amount of Soviet military production unknown, it's difficult to say exactly how much the Americans contributed.
With a little more digging, I can give you some estimates of what the Soviets attacked Berlin with and we can make some extrapolations from that. In 1945 it was estimated that the Russians had produced approximately 57,300 tanks (See Zaloga, Steven J., Jim Kinnear (1996). T-34-85 Medium Tank 1944–94, Oxford: Osprey Publishing.). According to this article on wikipedia 20,000 tanks and artillery pieces* were deployed to the battle. Among them were the Russian T34, SU-152, ISU-122 and the Iosif Stalin tank or the IS2. All of these were Russian tanks. Based on the known production numbers and the sheer force of Soviet troops mustered for the battle, it seems that roughly a third of the Red Army's tanks being deployed is not an unfeasible amount.
Further, eyewitness accounts of Soviet troops going into battle with nothing but tattered rags, the looted boots of SS troops clutching their battered Mosin-Nagant rifles lends credence to the idea I am suggesting. Namely that by the invasion of Berlin, Soviet troops had marched into the city with Soviet equipment, or the lack thereof. What they didn't have they did without. Even boots it seemed were scavenged from SS troops.
In short, if someone could find data on the total military prowess of the Russian industrial complex we could equate that to how much the Americans provided and determine if the American aide contributed significantly to Russian military operations leading up to the fall of Berlin. But bsed on my cursory research it seems unlikely that the Red Army derived such a significant advantage from US supply as to lend the quotation any real weight. It seems by 1945, the Soviets were on their own.
As a sidenote, the US lent over $31 billion to England, totaling over 60% of the Lend/Lease act.
*Although it is disputed by this site which cites Russian artillery pieces totaling 41,600. Note that while the Soviets made the trek to Russia they also encountered foreign tanks which were commandeered or joined the invasion of Berlin.
Though outside your time frame, this article details the termination of lend/lease a mere weeks after the capture of Berlin. Interpret it as you will.