A proposal to acquire real property or property rights within or outside of a lake or beach management district in accordance with RCW 36.61.020 is subject to the following limitations and requirements: (1) The real property or property rights proposed for acquisition must be in a county located west of the crest of the Cascade mountain range that plans under RCW 36.70A.040 and has a population of more than forty thousand and fewer than sixty-five thousand persons as of April 1, 2013, as determined by the office of financial management; and (2) prior to the acquisition of real property or property rights, the proposal must have the written approval of a majority of the property owners of the district, as determined by the tax rolls of the county assessor.