There is a prominent white line on the west side of Forge Lane visible on Google Earth’s 1945 aerial layer — see above — and it’s likely this is the cycle track mentioned in the Western Mail in 1937.
“FORGE LANE (Cardiff Road—Bassaleg Road), … is being reconstructed by Monmouthshire County Council and the Ministry of Labour,” reported the paper, adding that it “will be one of the first roads in Wales to have cycle tracks and dual carriageways.”