Late-lying snow is snow that persists and remains even after winter has ended and, in some areas, it persists into the summer depending on factors such as altitude; for example, in high mountainous regions. We have some late-lying snow in the area of Canada where I live. But that's because we are transitioning between winter and spring. Soon all of our snow will be melted and gone.

I agree with Terry. He probably answered your question best because he is Canadian. From where I am in the southern U.S., I have never heard the term in my life. We might say here something like, "left over snow."