Lee could not use chakra and thus could not perform any of the 3 techniques. However, Lee managed to pass the academy exam, while Naruto couldn't.
Why did Naruto fail when he could easily perform the Henge and Kawarimi and clearly had too much chakra for the Bunshin?
I believe Rock Lee was an exception, he excelled in Taijutsu to make up for his lack of skill in Ninjutsu and Genjutsu. Naruto on the otherhand initially started off bad at all 3 types of jutsus.
There also doesn't seem to be a formal exam, Iruka and the sensei's make the overall decisions hence why Naruto became a Genin despite failing the "true" exam.
Rock Lee is not the same year as Naruto. He would have graduated from the academy during the previous year. It is possible that the graduation requirements were not the same the previous year and thus Lee was able to pass.
When it came down to the decision for Naruto, it was a small panel of evaluators. One was Iruka--a close acquaintance of Naruto's--and another guy was for passing him (so he could manipulate Naruto to his own ends). The deciding vote was Iruka's alone, and it was Iruka that specifically insisted that Naruto must be able to create a plausible clone. The reason Naruto failed in that specific case is because of one particular man's expectations alone (to be fair, he had a pretty good reason). The general hatred the village had towards him, even despite the Third's orders, would likely have worked against him more generally. Lee would not have had that same hatred.
POSSIBLE SPOILER: The following makes use of some of the background of Might Guy that we only find out very late in the story.
The histories of Might Guy and Might's father give precedent to people exceptional at taijutsu being acceptable based on that alone. Exactly why is never really stated. We know that Might had troubles entering the school due to his poor non-taijutsu skills. Possibilities for advancement in these cases include:
Training so hard and demonstrating such exceptional skill that the village had essentially no choice but to recognize him. He, possibly like Lee, may have simply "skipped" the usual method to becoming a Genin.
A special case of the first point is that the ability to use the Gates is a rare, risky, and potentially extremely powerful skill. Possession of such a thing may be sufficient reason alone to advance in ninja ranks. This may both be as a precaution--make sure he knows how to use it lest we suffer for it--, or as a simple recognition of its usefulness when properly utilized. Naruto was not expected to have any control over the beast by default (only the upper echelons seemed to be aware of the possibility), which is in part why they feared him. The beast was only seen as a possible source of death and destruction, nothing more.
Might's father had an (entirely unexpected) epic last stand by virtue of taijutsu. Possibly word got out, and this led to a substantial improvement in the perception of taijutsu users. This may have created a special, taijutsu specific, path of advancement that was now available to Lee and Might.
Related to the previous: Advancement tracks for single-area specialists were already in place. Naruto was not a specialist in any specific thing. He was training under a more general program, which requires a broad range of skills but at less depth. Lee may have been under a specialist's program, which requires a narrow range of skills but at greater depth.
Might may have already had his eye on Lee, and may have used his stature and influence to push Lee through and into his team. We still need to consider a reason for how Might got his stature.
On possible INGAME explanation would be that Naruto is the Jinchuriki of the 9 tailed fox. Aside from the hate of the adults he HAS to pass EVERY test so that he is ready for what is coming for him.....as he out of all others will always be a target for enemy ninjas...a primary target even. That COULD be a possible ingame reason there.
Hate I would rule out as His most favorite teacher let him fail and that one didn't hate him at that time. _So its more probably the "you are not good enough yet for what troubles await ESPECIALLY you".
Out of universe that is one of the things that sadly make no sense...at least if you don't look at it with the stand that it makes "a cooler story". As even though Naruto was abmyssal in EVERY class at the academy and failed every test he should have passed. Why? He REGULARLY tricked anbu and kage with henges, he REGULARLY run from ANBU out of all things and managed to succeed! AND even hid from them with absolute ease! And then we see him sneaking up on and beating Sasuke into submission....all of that in the first episodes. And that despite him ALWAYS loosing to Sasuke and being said to be abmissal in EVERY shinobi class.
Why did Naruto fail when he could easily perform the Henge and Kawarimi and clearly had too much chakra for the Bunshin?
I believe that the 'too much chakra' explanation was a fan-theory.
To try and answer the question, I believe that the reason that Naruto passed is because he learned the Kage Bunshin technique. It is a much more complex (and dangerous) technique, which can be seen by the fact that is Forbidden technique. But even so, the Kage Bunshin is still a Bunshin technique.
That and he also helped to expose, defeat, and capture a traitor to the village.
