Well, at least I'm from a country that is neither Britain, Russia or America. So I would hope my opinions can be slightly less fuelled by nationalistic fervour than some of the opinions in this here thread.
If we're taking lend lease into account, and saying that no American involvement means no lend lease. I would assume that the same goes for the oil America was giving to Japan until it finally decided in 1941 that the army that was raping Chinese peasants weren't the nicest of buyers.
80% of Japan's oil at the time was from America, and I may not be an expert on the subject, but I assume that if we take American involvement out of the equation, and leave Japan with 80% less oil, they're going to have a lot of trouble. At least until they take over a few oil rich countries (which they did anyway after losing said American oil in real history), but the taking of said countries will be harder for them without the ability to so readily use the stuff that runs on oil, like planes, tanks and whatnot.
Now, on to lend lease itself.
I'm sure it helped, and it seems to be the base argument from the "yay" side of the argument, but I wouldn't consider it a pivotal aspect.
Lend Lease gave the other countries involved a little breathing space, in terms of costs. But with the exception of decent tanks sent to Britain, most of the hardware given could have been recreated by the country itself, even if it was at a cost. Britain would have eventually figured out how to make tanks that weren't pathetic and the Soviets would have quite easily been able to make a few hundred trains. I won't deny lend lease helped, but claiming it's the only reason un-America didn't wallow around in poverty seems a bit overzealous.
And again, noting the exception of tanks for the British, these lend lease vehicles had decent if not superior home-made alternatives.
Russians enjoyed the addition of American planes like the Aircobra and P-40, but they had also developed planes like the Yakolev and Mikoyan fighters, Sturmovik ground attack planes and Petlyakov dive bombers, all of which were very capable machines, which suffered early on due to the soviets horrendous command problems, but preformed on par with the Luftwaffe later in the war when Stalin realised that killing off experienced officers kind of damaged the ability for his army to be an experienced fighting force.
American tanks given to the Soviet union were generally regarded as inferior to stuff like the T-34 and IS-2 (And they were), which the USSR could churn out by the bucket load anyway.
British tanks, which really really sucked, were definitely inferior to American lend lease tanks like the Sherman. But I would think, that Britain realised it was severely lacking in the "tanks that don't suck ass" department and would have sought to fix that problem themselves if the easy and cheap option of getting some from America wasn't possible. They had a decent amount of time in which to do this as well, seeing as Hitler put operation sea lion on hold indefinitely after the battle of Britain.
British planes... I don't really have to say much about this do I?
I've already mentioned the battle of Britain.
Oh what the hell.
4,074 aircraft
casualties
2,500 killed
1,887 aircraft destroyed
1,963 aircraft
casualties
544 killed
1,547 aircraft destroyed
This is in 1940 by the way, before lend lease.
Britain does lose a rather sizeable amount of aircraft, and I assume that in history, Lend Lease might have been used to temporarily bridge the gap. But that wouldn't be necessary, as Germany certainly didn't know how large a proportion of aircraft Britain had lost, otherwise they would have continued. Britain could have safely repaired their aircraft numbers without more German attacks.
This has already been said by most of the fellows on the "nay" side, but again, just to hammer it home. The USSR was very much capable of defeating the German army. Early defeats were due to poor command, since Stalin killed off all his skilled officers in fear of them becoming skilled usurpers. That same early USSR also managed to lose a war against Finland. No offence meant to any Finnish fellows reading this, but it's just that you aren't the largest of nations, and yet, there's this. Still, later on the USSR got it's stuff sorted out and went on to take over as much of Europe as it could. I don't think lend lease was what fixed the soviet's command capabilities, so I will chalk this success up to the USSR itself.
North Africa was a front that might have suffered from the absence of American numbers and equipment, but depending on how fast Britain managed to fix it's tank problem, the African front could still be winnable, though it would take them a bit longer. The absence of America in the fighting sense would also mean that Australia and New Zealand would be less willing to have troops in Africa when the Japanese were closing in on their homeland, so North Africa would also lose those troops. Which leaves them with Canadians, free French, free Polish and Indian troops.
I suspect, that the Japanese would attempt to invade Australia and New Zealand at some point, especially Australia. But I think they might run into a bit of trouble in the latter, seeing as Australia's wildlife and environment alone could probably deal a significant blow to Japanese forces. New Zealand would not fare so well, we're a small country, most of our planes were from lend lease, our navy is tiny and we had only seven or eight coastal guns spread across the whole country. Unless Australia decided the help (and they probably would, after a period of pointing and laughing) we would be pretty screwed.
Australia and New Zealand (if not taken over) would still be semi-capable of at least holding off the Japanese by themselves. Once Germany surrenders, Russia (if they hadn't already) would then turn their attention to Japan, and the results of the soviet invasion of Manchuria in 1945 suggests that they would slaughter them.
This is all speculation, but I consider the possibility of the axis ever winning ww2 to be laughable.
Italy couldn't fight to save itself, and the USSR or Britain by themselves could easily mop the floor with the minor axis nations like Romania and Bulgaria. So what it really boils down to is Germany and Japan fighting Poland, Australia, France, Canada, Britain, South Africa, New Zealand, Czechoslovakia, Norway, Belgium, Luxembourg, Netherlands, Greece, USSR, China, Yugoslavia and India.
In terms of fighting wars, Germany has had a long history of being complete baddasses and winning with inferior numbers. But in this case, it's a little too much of a number gap, even without the US.