You can look up the duty. The tariff tables are available online. Japan has most-favored nation status, so the duty on a lens imported from Japan should be comparatively low. I did a quick look-up and the HTS (tariff) code is 90021190. The duty rate should be 2.3%. This should also be the case for most lenses of Asian manufacture that may be legally imported to the U.S.. The big exception is Singapore where no duty is collected.
Duty is due at the border and is paid by the importer (you). The exporter cannot do this for you. Customs will hold your goods at the border until duty is paid. You can contract for a customs broker to take care of the details. That is one advantage of using a shipper such as UPS as opposed to sending the item via international air mail. UPS will charge a premium price however for this service.
Duty is assessed based on the value of the goods. Value can be determined a number of ways. These include what you paid and what it might sell for in the U.S.. Generally, price paid is the norm unless it seems unreasonably low.
There may be a exception for items imported for personal use under a certain value, though I am not up on those regulations. Here is a link to the U.S. Customs and Border Protection Web site:
CBP.gov - home page
You might be interested in the "not purely legal" ploy used by resellers of Russian goods. You have a private individual in another country to make the purchase. They send you the lens duty-free via international e-mail as a "gift". This is a good thing for Russian lenses since the duty on lenses from there is 45%. Ouch!
Steve
(My last job was customs-related...)