The Â£1.5m grant is to repair and refurbish business premises along Kirkgate and start a feasibility study on the cloth hall's restoration.
It is a "fragile" Grade II* listed building that needs considerable investment, Leeds City Council said.
It is hoped some of the improvement works could start in the summer.
Along Lower Kirkgate the buildings are mainly 18th and 19th Century three-storey terraced properties.
The cloth hall is the "most important building" on that part of the street, the authority said.
It hopes to see if the restoration can be carried out in a "financially sustainable manner".
The building was built in 1711 as a covered market for the sale of cloth.
Surveys, conservation and archaeological investigations would lead to a feasibility study and further consultation on the eventual repair of the building.
A lottery grant is to be used to restore parts of an historic street in Leeds and help conserve the city's "important" First White Cloth Hall.