Does Tibet have much rain in May? I want to go to Lhasa, Namco and Linzhi. About fifteen days. Who can recommend scenic spots, routes and general consumption? Say "no"

May should be fine. You can spend less than 15 days in these three places. A week is about the same. If you add the round-trip time, you can see for yourself how many days it will take on the road.

If you have enough time, you can consider carpooling and take a small loop-Linzhi-Gyangze-Everest-Shigatse-Namco-Lhasa.

Go back and don't waste time. You have almost all the places you want to go. The rest of the time can be spent herding sheep, sunbathing, drinking tea and wandering around in Lhasa.