USA citizen asking about visa requirement for tourist visa

A China tourist visa is required for you to visit Tibet Lake Manasarova. From June to July, Tibet is not open to foreigners because of 60th Anniversary of Tibet Liberation. You can visit it in August. But before you apply for China visa, you should get a Tibet Entry Permit from Tibet Tourism Bureau, it is required when you submit application. You can contact a travel agency in China to get it for you, then send it to you in USA.

If you don't want to get the Tibet Entry Permit, there is another option, you don't write that you will visit Tibet on the visa application form, you can write that you will visit Xian, Shanghai, etc, then it is easy for you to get a Tourist Visa (L) to China, once you arrive in China, you can ask a travel agency in China to apply the Tibet Entry Permit for you (you can also ask the agency to get it before you arrive in China), at last, take the Tibet Entry Permit and China visa to visit Tibet.

If you fly down to Kathmandu, it is possible for you to get a visa from China embassy in Kathmandu, you'd better find a travel agency to do it for you. The agency can get Tibet Entry Permit and China visa for you.