I would not do this.
It has been possible in the past, but the last person I heard from who cycled through Tibet started in Kashgar... the ONLY reason he was allowed to continue was by paying "fines" at every checkpoint, as it would have been too much trouble to deport him by truck thousands of kilometers away. From Yunnan, they would be more inclined to take action, and the checkpoints along the eastern border are not "3am roll-throughs" anymore.
Keep in mind that even if you speak good chinese and you can somehow get away with it, it is still illegal... and can still land you in a PRC holding cell awaiting deportation, and can still result in loss of your gear (anything the Chinese deem confiscable) if anything goes awry.
That said, my information does come second-hand.
One of the reasons China has such a lockdown on Tibet is because of uncontrolled foreign influence. Doing this just substantiates and perpetuates this reason. If people start playing by the rules (however unfortunate) perhaps the borders will open once the Chinese government is assured that there is no more "subversive" activity going on. This is the same kind of thinking that HH made himself unpopular with, and angered many Tibetans willing to fight for independence. So be it. Please be advised that this is a politically sensitive issue, and a politically sensitive region. I would advise anyone to think twice before doing anything that would make it worse.
There are organized tours from Lhasa to Kathmandu (you can look them up online). You need a tourist travel permit to the Lhasa area. Once in Lhasa, hook up with your tour group. Get proof of your tour plan and take it to a government office for a permit to travel outside of Lhasa. The next time you should have to worry about this is at the Tibet/Nepal border. This presupposed that you have a Chinese tourist visa valid for the amount of time it will take to get to Nepal.
Good luck! I know one other person on the board here has done a similar trip recently, and another is planning one next year after his ankle heals up. Maybe they can give you more info.