Lurchers are technically a cross between a sighthound and any other breed, though typically they are crossed with herding dogs or terriers. The crosses are intended to produce a dog with characteristics of both breeds, typically a blend of speed (from the sighthound) with intelligence/biddability (from the pastoral breed) or hardiness/tenacity (from the terrier). They aren’t a breed in the true sense, but a specific class of crossbreeds which have been bred for several hundred years for various tasks. It’s thought that originally they were first bred to get around laws banning commoners from owning sighthounds in England and Scotland, but have endured as a more adaptable, trainable option for a hunting dog than a traditional sighthound.
I tag them as sighthounds since they’re always a sighthound cross often with very noticeable sighthounds traits, but I’m not sure if they would be technically considered true sighthounds.