Gates open = LEE
Not open= Neji

Without gates open I would give it to Neji, Neji isn't as fast as lee, but he would be fast enough to get some hits in, and unless you have instant demon fox healing, with nejis style it only takes a few hits.

As was already said Lee with gates open would beat Neji, but also at the cost of his own health. Ripped and torn muscles, however nothing like the condition he’s in now.

You need to remember that just 1 year ago lee was perhaps the worst genin ever, but after all his training he's on par with some jounins.

No one had ever injured Gaara including any of the elite assassins Gaaras father sent after him. Which were no doubt atleast chuunins if not jounins

Give a fully healed lee 6 more months of training, and he won't need to open his gates to beat Neji.