§ 556. Acquisition of lands by the city for the project. The city shall have power to acquire by purchase, or by condemnation in the manner provided by chapter twenty-one of the Greater New York charter, title in the name of the city to any lands, easements, or rights in land not owned by the city on the seventh day of April, nineteen hundred thirty-three, which may be required for the project, and payment therefor, and for any lands theretofore acquired but not paid for by the city, shall be made by the authority. The power hereby conferred upon the city shall not limit or restrict the power of the authority itself to acquire lands, easements, or rights in land in the name of the city.