Lepus is a constellation lying just south of the celestial equator, immediately south of the constellation Orion. Its name is Latin for hare. While Hellenic mythology is not chuck full of hares, Lepus was indeed one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and it remains one of the 88 modern constellations recognized today.

The only ancient writer I have found who mentioned the constellation Lepus by name and myth is Hyginus, but to make up for it, he gives us a lot of material to work with. Lets break his words down, shall we? From the Astronomica:

"Some say that it was put there by Mercury [Hermes], and that it had been given the faculty, beyond other kinds of quadrupeds, of being pregnant with new offspring when giving birth to others." [II.33]

Well, there is not much to say against that, now is there? I looked it up, and it seems that hares have about three times three+ young every year, and European hares are, indeed, capable of carrying two litters.

"The hare is said to be fleeing the dog of the hunter Orion, for when, as was proper, they represented Orion as a hunter, they wanted to indicate what he was hunting, and so they put the fleeing hare at his feet. [...] Those who disagree with this reason say that so noble and great a hunter as Orion (we spoke about him in the discussion of Scorpio) shouldn’t be represented hunting hares. Callimachus, too, is blamed, because, when he was singing the praises of Diana [Artemis], he said she delighted in the flesh of hares and hunted them. So they have represented Orion fighting the Bull." [II.33]

Orion (Ὠρίων) was a famed hunter who has a lot of mythology to his name. He is also included in a lot of existing mythology. The constellation Canis Major might represent his entire pack or one of them, who are/is eternally pursuing Lepus the Hare or helping Orion fight Taurus the Bull. In the prime of his life, Orion joined with the Goddess Artemis and Her mother Leto, for an epic hunt in which Orion threatened to kill every beast on Earth. Gaea revolted and sent a giant scorpion to kill Orion. Orion, although very powerful, was overcome by the creature, but Artemis and Leto requested to Zeus he'd be immortalized in the night's sky. The Scorpion was admitted into the heavens as well, along with his hunting pack... and the hare.
Kallimachos' wonderful hymn to Artemis does, indeed, include the hare:

"Artemis we hymn – no light thing is it for singers to forget her – whose study is the bow and the shooting of hares and the spacious dance and sport upon the mountains." [1]

Hyginus has one more story to share, which comes not from the realm of mythology, but the realm of folklore.

"The following story of the hare has been recorded. There were no hares on the island of Leros, and a certain young man of the state, led by a liking for the breed, brought in from another country a pregnant female, and watched over her very carefully as she bore her young. When she had borne them, many of the citizens developed an interest, and by acquiring some for money, some as gifts, they all began to raise hares. In no long time such a multitude of hares was produced that the whole island was swarming with them. When men gave them nothing to eat, they made inroads on the grain fields and devoured everything. The inhabitants, faced with disaster because of this, since they were reduced to hunger, by co-operation of the whole state were said at length to have driven them from the island, through with difficulty. So afterwards they put the image of a hare in the stars, that men should remember that there was nothing so desirable in life but that later they might experience more grief than pleasure from it." [II.33]

The constellation Lepus is visible at latitudes between +63° and −90°, and best visible at 21:00 (9 p.m.) during the month of January.