Tibet is part of Mainland China so once you're in you can pretty much go wherever you want. You will need a Chinese visa in order to enter Tibet plus a tourist permit to visit Tibet. The agency in Nepal should be able to sort out the visa and permit.
I travelled by 4x4 in Tibet from Lhasa to Everest Base Camp and that took 4 days. It's a further days travel to Nepal from there, maybe not if you avoid going to base camp. From Lhasa you can go by bus, train, plane to the rest of China. In theory if you took the train you could get to Beijing in 2 days.
I flew from Lhasa to Zhongdian in Yunnan province and headed south to Kunming and then onwards to Laos. If you wish to travel to Vietnam then you'll need to head further east to Nanning and go by bus. Don't think the train is running.
Perhaps someone can comment on the Nepal side of thing?
Edit: Safety shouldn't be a problem. The Maoists in Nepal have had a ceasefire for the last 6 months and as of today signed a peace deal. Good news
