Whenever, in the opinion of the lake board, any special assessment is invalid by reason of irregularities or informalities in the proceedings, or if any court of competent jurisdiction adjudges such assessment illegal, the lake board, whether the improvement has been made or not and whether any part of the assessment has been paid or not, may proceed from the last step at which the proceedings were legal and cause a new assessment to be made for the same purpose for which the former assessment was made. All proceedings on that reassessment and for the collection of the assessment shall be conducted in the same manner as provided for the original assessment. Whenever an assessment or any part of an assessment levied upon any premises has been set aside, if the assessment or part of an assessment has been paid and not refunded, the payment shall be applied upon the reassessment.