The answer is, there is no Lake Hazel, but there was once. Sort of.
Back in the early 1900s there was a move to create reservoirs to capture Boise River water for irrigation purposes. Potential water users contracted with David R. Hubbard, a local land owner, to excavate reservoirs called Painter Lake, Hubbard Lake (later Hubbard Reservoir), Kuna Lake, Watkins Lake, Catherine Lake, and Rawson Lake. These were to be connected by laterals. All except Rawson Lake were completed. In the meantime, the much larger Boise Project came along with the promise to bring irrigation to the valley. The lakes were abandoned because they would likely interfere with the Boise Project. Since they were not being used for water storage, all the "lakes" disappeared in later years, except for Hubbard Reservoir.
So, what does all this have to do with Lake Hazel? Painter Lake was renamed Lake Hazel at some point. Even with the new name it was fated to be a lake in name only, with no water in evidence.
Thanks to Madeline Kelley Buckendorf, who did the research on this for a National Register of Historic Places application I found from 2003.