If the connection with the sewer, main, wire, or conduit is not made by the owner of the property within the time specified in the notice given by the city auditor, the governing body shall order such work done by such person as it may contract with therefor at the expense of the lot or parcel of land adjoining each improvement or service connection. Such work shall be administered and observed under the supervision of the engineer acting for the municipality. The expense of making such connection, including the expense of giving all notices relating thereto, of making the assessments therefor, and of any other nature, shall be assessed by the engineer against the lot or parcel of land properly chargeable therewith, and the assessment list shall be filed in the office of the city auditor. The city auditor shall cause such list, together with a notice of the time when and place where the governing body will meet to consider the approval thereof, to be published in one issue of the official newspaper of the municipality at least ten days prior to the meeting of the governing body at which the approval of the assessment will be considered.