When the L-train tunnel closes for repairs in 2019, disrupting subway travel between Brooklyn and Manhattan for 225,000 daily commuters, the city will look to the lowly, human-powered bicycle to be a part of the solution.

A new five-year New York City transportation plan includes a proposal to create protected bike lanes on a section of Delancey Street on the Lower East Side that connects to heavily used bike lanes on the Williamsburg Bridge.

The...