Whenever in the opinion of the city council of any city the public interest or convenience may require that body to order the improvement of any street lighting system located on lands in the city outside the boundaries of a district established under the provisions of this part, whether or not such lands are contiguous to the boundaries of such established district, that body may, in lieu of establishing a new district under this part, order the annexation of such lands to an existing district established under this part and may assess, either partly or wholly, the costs and expenses, including all incidental expenses of such improvement, or of any one or more of the items thereof, upon the lands in the district, including the lands thus annexed.