There have been many posts regarding this issue, but this is a question that can't have an accurate answer. It's a hypothetical which would make it better suited for /r/historicalwhatif. We can look at the US' contributions to the war and determine the global impact of US involvement. However, what I will provide is some insight into strategic importance and you will have decide how significant those involvements are, considering this is a hypothetical question. Most of what I will discuss will be regarding the Pacific theater.

there is one thing we can say for near certainty. Had the US not joined the war, Australia and New Zealand would have very likely been occupied by Japan. At the rate in which Southwest Asia fell, and the Royal Navy's difficulty in controlling the Indian Ocean, meant that Australia was left to their own defense. Not only that, but most of the ANZAC troops were in North Africa fighting the Italians and Germans for the UK. So what was left for defense was largely militia. Don't get me wrong, the Australians fought valiantly and since this is all speculation, they certainly would have given the Japanese a headache had they become an occupied nation. But the US intervention diverted those landing forces to Guadalcanal. The allied naval fleet, called the Watchtower task force, was composed of 75 warships and transports. This task force was composed of both US and Australian warships, however this is significant because this task force was still forced to withdraw upon meeting the Japanese at the Battle of the Eastern Solomons. It's fair to say that the Australian Navy alone could not stop the Japanese fleet alone. The Battle of Guadalcanal was important, because the Japanese were utterly defeated on land after making dozens of landings and many air raids against the entrenched US troops. This battle effectively eliminated any chance of japan to invade Australia. So, in the eyes of the Australians, yes US intervention was "as important as the US likes to think they were."

Secondly, the US entrance into the war led to a historically significant agreement between Japan and Russia. Before the US entered the war, Japan and Russia were having a rather bloody border skirmish in Manchuria. Northern occupied China was a staging ground of Japanese forces to attack the Russians in Manchuria, which caused them to divert a lot of troops to the far east (this pre-dates Barbarossa, mind you). the treaty was called the Soviet–Japanese Neutrality Pact. It's important to not that this wasn't in direct result of US involvement, but I will quote the japanese alterior motive for coming to terms with Russia:

"In 1940, with the defeat of France and the subsequent expansion of the Axis Powers, the Soviet Union wished to mend its diplomatic relations in the Far East in order to safeguard its eastern border and concentrate on the European theatre of war. On the other hand, Japan, bogged down in a seemingly interminable war with China and with diplomatic relations with the United States rapidly deteriorating, sought an accommodation with the Soviet Union that would improve its international standing and secure the northern frontier of Manchukuo against possible Soviet invasion."

So the threat of a war with the US was a reason for the Japanese to come to terms with Russia. This is significant, because those forces that Russia had stationed near Manchuria, were sent to Moscow and are credited with reinforcing the Mozhaisk defense line just in time to bog down the German advance. The city was never taken, however had those reinforcements never came from the East, who knows what could have happened. Moscow could have been taken, German Army Group Center could have been transferred to Stalingrad, while Army Group North could have kept their panzer divisions to strangle Leningrad. It's is very arguable to say that the US indirectly effected Russia's ability to reinforce Moscow.

All of this doesn't take into account the US' contributions in Lend Lease, North Africa, China, Burma, Italy, France, Germany, etc. Since this is an opinionated hypothetical question, I would say yes. The war may very well have been lost had the US not had a stake in the conflict.

Without US involvement? Considering that US involvement included selling weapons to nations who paid cash, Traded 50 destroyers in exchange for british bases in the lend-lease program.

The most important thing to remember is that the US had the production facilities, and the men, to supplement the allies. Millions of tons of food was sent to the Allies. Hundreds of thousands of men also participated in the European front.

Trucks were shipped to the Russians, who used them to transport men, and converted for weapon use. Thousands of tanks and tank destroyers were shipped as well http://ww2-weapons.com/History/Production/Russia/Lend-Lease.htm

The British at the beginning of the war were effectively alone. The French were forced to surrender in 1940 after the capture of Paris.

Would the Axis have won if the US had not intervened in ANY way? More than likely. If the US had never sent ground forces, it is more debatable.

Would the war have been lost without US involvement?

Reminder to respondents that "what if" scenarios are not entertained in this sub. Here are the relevant rules:

1. Is this the right place for your question?

2. No speculation