A lurcher is a crossbred dog resulting from mating a greyhound or other sighthound with a dog of another type such as a herding dog or a terrier. The lurcher is not a "breed," but is a generic descriptor of a group of varying dogs. It was for hundreds of years strongly associated with poaching; in modern times, it is kept as a hunting dog or companion dog.
Lurcher
Lurcher, illustration from The Sportsman's Cabinet by William Taplin, 1803; engraved from a painting by Philip Reinagle
Dog crossbreeds, sometimes called designer dogs, are dogs which have been intentionally bred from two or more recognized dog breeds. They are not dogs with no purebred ancestors, but are not otherwise recognised as breeds in their own right, and do not necessarily breed true.
A Labradoodle is bred from a Labrador Retriever and a poodle.
Greyhound/Old English Bulldog first cross
Greyhound/Old English Bulldog second cross
Greyhound/Old English Bulldog third cross