When all owners must agree to a refunding plan

If the petition is filed and acknowledged by the owners of assessment units representing one hundred percent of the unpaid assessments in any improvement district, and by all lessees of any assessment unit to be assessed, who, by the express terms of their respective leases must pay the kind of assessments contemplated by this article, unless the lessor of such lease files with the petition a duly acknowledged waiver of the stipulation in the lease which requires the lessee to pay such special assessments, and a written undertaking by the lessor or owner to pay the special assessments to be made under the proposed refunding plan, then the council shall proceed as provided above to have a hearing on the proposed new method of assessment and the assessment roll; provided that in case the owners of assessment units representing one hundred percent of the unpaid assessment as provided in this section consent, in writing, to the amount and apportionment of the proposed assessments under the refunding plan, it shall be unnecessary to give the notice or to hold any of the hearings specified above and the council may immediately proceed to fix the assessment in the manner provided; and provided further that the council may by resolution require the petitioners to deposit with the director of finance, within seven days after adoption of such resolution, a sum sufficient to meet the cost of the refunding project as reported by the director of finance, in which case the holding of the public hearing (if applicable) and any other actions of the County with respect to the refunding shall be conditioned on the making of such deposit within such period.