How could Sasuke match Lee's speed? In episode 22 of Naruto, when Lee fights Sasuke, we have seen Lee open the first Gate, after which he claims to have supreme speed to launch his attack.  

But (not far away) in episode 66, Sasuke obtains that speed, within only a month of training, while it took Lee many years of extremely hard work.  

Although he had Sharingan, it doesn't mean that he can copy the speed of his opponent. How was it possible?
Sasuke:
is a "genius" (possesses innate talent).
is a Uchiha (somewhat the reason why he is a "genius").  
Lee:
is a hard worker (his main motivation being to surpass Neji, the "genius" in his team).  


Basically, Lee has no innate talent to ninjutsu or genjutsu. Thus he had to master taijutsu in order to surpass the "geniuses", and become a great ninja. This is a process that takes a lot of time.
Sasuke on the other hand does not need to work so hard in order to accomplish what Lee needs to work on for several years. Remember that he was able to master the Goukakyuu no Jutsu at a very early age.