why is your lap called what it is?

[Bluecat]

so why is your lap called your lap?

[mollykins]

Why's a nose called a nose?

[boxtops]

from the middle English Lappen, a fold or wrap - which is presumably why cats lap milk, they have to curl their tongue into a scoop to lap it up.

[Clanad]

Well... one lap is a noun and the cat's action is a verb, so they have differing backgrounds.

Lap, as in front of your behind is described thusly in On-Line Etymology Dictionary:

O.E. læppa "skirt or flap of a garment," from P.Gmc. *lapp- (cf. M.Du. lappe, O.H.G. lappa, Ger. Lappen "rag, shred," O.N. leppr "patch, rag"), from PIE base *leb- "be loose, hang down." In 17c. the word was a euphemism for "female pudenda." Sense of "lower part of a shirt" led to that of "upper legs of seated person" (late 13c.).

Whereas to lap has this reference:
"take up liquid with the tongue," from O.E. lapian, from P.Gmc. *lapajanan (cf. O.H.G. laffen "to lick," O.S. lepil, Ger. Löffel "spoon"), from PIE imitative base *lab- (cf. Gk. laptein "to sip, lick," L. lambere "to lick"). Meaning "splash gently" first recorded 1823, based on similarity of sound.

And, lest we forget, lap has another verb form, maenin to run so fast as to pass the leader twice:

"to lay one part over another," early 13c., from lap (n.). The sense of "to get a lap ahead (of someone) on a track" is from 1847, on notion of "overlapping." The noun meaning "a turn around a track" (1861) is from this sense. Related: Lapped; lapping; laps.