Drill Responsibly in Leased Lands Act of 2008

Drill Responsibly in Leased Lands Act of 2008 - Amends the Naval Petroleum Reserves Production Act of 1976 to direct the Secretary of the Interior to conduct an oil and gas competitive leasing program in the National Petroleum Reserve, Alaska, that includes at least one lease sale each year during the period 2009 through 2013.

Instructs the Secretary of Transportation to: (1) facilitate pipeline construction to transport oil and gas from or through the National Petroleum Reserve in Alaska to existing transportation or processing infrastructure on the North Slope of Alaska; and (2) require certain authorized pipeline operators to certify annually that the pipeline is being fully maintained and operated in an efficient manner.

Directs the President to coordinate with oil and natural gas producers on the North Slope of Alaska, and other specified entities, to expedite construction of a natural gas pipeline from Alaska to U.S. markets.

Amends the Mineral Leasing Act to repeal provisions authorizing the export of Alaskan North Slope oil.

Amends the Export Administration Act of 1979 to reimpose the prohibition against crude oil exports.

Prohibits the Secretary of the Interior from authorizing any new lease for exploration or production of oil or natural gas unless the lessee: (1) certifies for each existing lease that the lessee has diligently developed the pertinent federal lands in order to produce oil or natural gas, or is producing oil or natural gas from them; or (2) has relinquished all federal oil and gas leases that are not being diligently developed.

Instructs the Secretary to ensure that lessees under leases for exploration, development, and production of oil and natural gas on federal lands make prompt, transparent, and accurate royalty payments.