If the jury, or the court if jury be waived, finds the outlet and drainage sufficient it shall assess the damages sustained by the lands in the lower drainage district or districts by reason of the improvement, together with awards for damaging and taking lands for rights-of-way required, which shall be paid by the irrigation district in the same manner as such payments are made in establishing the system in the irrigation district, and the cost of improving the lower system or systems to the extent the improvement benefits lands in the irrigation district shall be assessed to the lands in the irrigation district as other costs of drainage improvement are assessed.