New York City’s tax on luxury second homes is giving city lawmakers new leverage to pursue an overhaul of its property tax system that elected officials acknowledge is outdated, but are loath to take up.

The city must come up with a new valuation method for condos and co-ops that would take effect in 2028 or risk fencing off thousands of apartments from the new surcharge projected to generate $500 million annually.

The pied-à-terre tax is being levied on nonresidents with one- to three-family homes assessed at $5 million or more by the city Department of Finance, and on condos …