If any lands in any district organized under this act on which benefits have been appraised and confirmed, are not liable for assessment at the time of the execution of the work, but afterwards during the period when such work is being paid for, become liable to taxation or assessment by reason of some change in condition or ownership, such lands shall thereupon be assessed as other lands in said district receiving equal benefits. Providing that lands owned by Indians, by the State of Oklahoma, or any political subdivision, or any school district, shall be assessable under this act; provided, however, districts established under this act are authorized to enter into contracts providing for payment in lieu of assessments on any such lands. Any assessments made on lands previously exempt shall not be retroactive or cumulative, and such lands shall be assessed, proportionate to the benefits appraised thereon, for the remaining time required for payment of the cost of such work.