All lands, including school lands, granted lands, escheated lands, or other lands, held or owned by the state of Washington in fee simple (in trust or otherwise), situated within the limits of any assessing district in this state, may be assessed and charged for the cost of local or other improvements specially benefiting such lands which may be ordered by the proper authorities of any such assessing district and may be assessed by any irrigation district to the same extent as private lands within the district are assessed: PROVIDED, That the leasehold, contractual, or possessory interest of any person, firm, association, or private or municipal corporation in any such lands shall be charged and assessed in the proportional amount such leasehold, contractual, or possessory interest is benefited: PROVIDED, FURTHER, That no lands of the state shall be included within an irrigation district except as provided in RCW
87.03.025 and
89.12.090.