I did some hunting and found nearly 20 different businesses in Lubbock that allow you to bring your pet inside. Some are chains that have a company-wide policy allowing pets, but others vary from store-to-store. So, I double-checked and called any that were uncertain to make sure.
Thankfully, Lubbock has a variety of great options for snow cones and shaved ice. From bigger businesses with multiple locations, to small hole-in-the-wall mom and pop shops, there is something for any and every taste.