I am a Romanian citizen and would like to visit China and Tibet for 2 weeks in total.

The travel permit to Tibet is not related to the tourist L type to PRC. You need to apply for a tourist L type to PRC first. After you enter PRC, you need to find a travel agency to apply for the Tibet Travel Permit for you. And then you need to book a tour to visit Tibet. In principle, it’s free of charge, but the travel agency will charge the service fee and it varies for different agencies.
AS for the tourist L type to PRC, you need to provide your passport and its copy, the completed application form attached with a passport-style photo, hotel reservation and round trip air tickets to apply for it. It costs 240 Leu. When you apply for the tourist L type, you’d better not mention your plan to visit Tibet.