Ive owned more terriers and spaniel bitches than lurchers mate, only one lurcher bitch, but i dont expect the lurcher to have problems that the others wouldnt get... aye some get huffy and stroppy, some go quiet, but again, like has been said, once out working, its all forgotten. Id never take a bitch in season around other working dogs, and iv got a bitch that will snap at other bitches when in season, so i tend to work them alone or with trusted bitches they get on well with.
None of mine have had a phantom so im not sure, but id probably keep them in for a bit, especially if they went fat