According to Wikipedia, a lurcher is a cross between a sighthound and any other breed. A sighthound is a hunting dog that hunts primarily by sight and speed, rather than by scent and endurance (which is what scent hounds do). The greyhound and the whippet are classic examples of sighthounds.
The dog that the sighthound is crossed with (Wikipedia adds) is "most commonly a pastoral breed or a terrier type of dog." The collie is a typical pastoral breed, and Wikipedia notes that "collie crosses are popular, given [that] the working instinct of a sheepdog when mated with a sighthound gives a dog of great intelligence plus speed". So a lurcher is often a cross between a greyhound and a collie, but not necessarily so.
Wikipedia further adds that "[h]istorically a poacher's dog, lurchers in modern times are used as pets, hunting dogs and in racing."
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