Tibet travel regulation clearly states, no independent travel is admitted for international travellers in Tibet. So you will have to arrange a package Tibet tour with a local Travel agency in Lhasa. Including the Tibet travel permit. It is your Tibet travel agency that applies for your permit. Tibet Tourism Bureau issues the permit.
So, the answer is no. You cannot apply for a Tibet travel permit directly. It is your travel agency going for you. It takes 20 days to make Tibet travel permit. Therefore you will have to choose your travel agency wisely.
We know many fictitious travel agencies are claiming to be locally owned in Tibet. Which many are not based here in Lhasa? Let alone with registration with Tourism Bureau here. Hence we would like to recommend you a smaller effective travel agency in Lhasa for more attention.
You can book your tour with us for a better Tibet travel experience. Our company is found in the year 1997. With these many years of experience come with a much-need reputation and love from around the globe. We are one of the few oldest existing travel agencies in Lhasa. You can find lots of good reviews from our clients on our TripAdvisor page.