For such a phrase cf. (e.g.) 'bull's blood' under theta 124, nu 539, tau 156. Mentions of 'hare's blood' are much rarer, but the medical writer Soranus (C1 C.E.) twice (1.52.2; 2.26.3) refers to 'hare's flesh' (κρέας λάγειον ), amongst other wild meats, and the C13 Lexicon of pseudo-Zonaras (lambda Page 1288, line 22) has 'hare's: blood and flesh,' apparently combining Soranus and the Suda. Once separated from its medical context, the adjective seems to have become a bit of lexicographical flotsam.
For hares cf. generally lambda 16, lambda 26, lambda 27, lambda 28, lambda 29, lambda 30, lambda 31. And note generally J.R. Sallares, The Ecology of the Ancient Greek World (London 1991) 20: 'The rabbit (Oryctolagus cuniculus) is native to the Iberian peninsula. It was unknown to classical Greek authors, such as Aristotle, and was perhaps still rather unfamiliar to the inhabitants of the eastern Mediterranean as late as the time of Galen. The hare (Lepus europaeus) existed instead in classical Greece'.