I work with a breed-specific rescue ; there are as many kinds of temperament and exercise requirements as there are lurchers, depending on what the particular cross of dogs is. The one thing they all usually share is a terrific capacity for finding the most comfortable sofa and spending hours on it snoring in strange positions.
There are also a number of different shapes; their 'build' is actually a plus-point. Sighthounds (greyhounds, whippets, deerhounds, salukis, sloughi, azawakh, wolfhounds, borzoi, Ibizan hound, podenco, galgo, those I've forgotten and any mixture thereof) are one of the oldest types of dog existing and in general one of the least messed about by the show-ring types. The showing brigade have sadly had a go with the greyhound and it isn't pretty but as a rule, the form follows function. They're made to run; they have deep chests, long, straight legs and a nipped-in waist or tuck-up which allows them to fold and extend when they run. They have the predator's large eyes, and long snouts (for efficient air intake); salukis have webbed feet for ease of crossing the desert.
Within those general parameters you'll find dogs who are long and lean, dogs who are 'cobby' and quite chunky. Dogs with hardly any hair and dogs you have to wait until they move to know which direction they're facing. Dogs who are wildly excited by everything and dogs who are hardly ever excited about anything. Dogs with tremendous prey-drive and dogs who hunt only what they can blag from their humans at dinnertime. Dogs who are barky and dogs who are silent.
I'd recommend reading a book called 'The House Lurcher' by Jackie Drakeford which has some very sensible advice for lurcher owners. If you fancy a laugh I'd also Google John Linwood Grant's Greydogtales and read his articles on living with lurchers which, while funny, are SO true.