I have had several rescue Lurchers over the years. Best dogs ever imho, but worth bearing in mind that different breed mixes result in very different types, so if you do ever consider getting one it’s worth doing some research about which type would best suit your family. Very rough examples being, Collie mixes can tend towards the brainer side, easier to train, but also more likely to get up to mischief, Salukis mixes tend to be more sensitive and/or needy. Those from working lines will be more prey driven, as will rescues that have potentially already worked.
Both the ones I raised from pups had great recall and were whistle trained, so could go off lead, but I still chose where I let them off carefully, as two or more Lurchers in full flight, whilst stunning to watch, can be a bit full-on for a lot of other dog walkers! 
There are so many in rescue centres all over the country, but also specialist rescues like Lurcher Link, Lurcher SOS, EGLR etc. They do get pups in (two of mine were very young pups when the rescues took them in) but don’t usually list them as available because they go so quickly. It’s worth joining their FB pages for early info on dogs as they come in. There are well known Lurcher breeders too, but why would you buy one when there are so many in rescue?