Regions of melting snow at various altitudes can result in vertical circulations that enhance vertical motion and increase precipitation intensity. The explanation of these types of circulations is a bit technical. For those with a greater interest in weather, the names of a few articles are listed in the references at the end of this discussion.
Could a melting layer near the ground due to the influence of a warn lake result in a circulation that enhances the precipitation near the rain-snow line observed at the surface? If so, some immediate problems arise with identifying radar evidence. Water-coated ice produces stronger reflectivity on radar than surrounding precipitation of similar intensity. In the case of Duluth, MN, orographic lift, convergence at the head of Lake Superior, and other related processes can enhance precipitation in the same area as the melting-induced circulation if that circulation develops. Radar signatures of the circulation's effects could easily be masked or distorted.
A more in-depth discussion targeting the Duluth, MN area will be written after more personal study is done.