Etymology
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lap (n.1)

Old English læppa (plural læppan) "skirt or flap of a garment," from Proto-Germanic *lapp- (source also of Old Frisian lappa, Old Saxon lappo, Middle Dutch lappe, Dutch lap, Old High German lappa, German Lappen "rag, shred," Old Norse leppr "patch, rag"), of uncertain origin.

Sense of "lower front part of a shirt or skirt" led to that of "upper legs of seated person" (c. 1300). Used figuratively ("bosom, breast, place where someone or something is held and cherished") from late 14c., as in lap of luxury (which is first recorded 1802). To drop or dump something in someone's lap "shift a burden" is from 1962. From 15c.-17c. the word (often in plural) was a euphemism for "female pudendum," but this is not the source of lap dance, which is first recorded 1993.

To lap dance, you undress, sit your client down, order him to stay still and fully clothed, then hover over him, making a motion that you have perfected by watching Mister Softee ice cream dispensers. [Anthony Lane, review of "Showgirls," New Yorker, Oct. 16, 1995]

Lap-clap was old slang for "an act of coition" (c. 1600), in warning expressions to youth often paired with lip-clip "a kiss." Also compare slang Lapland "the society of women."

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lap (v.1)
"lick up (liquid), take into the mouth with the tongue," from Old English lapian "to lap up, drink," from Proto-Germanic *lapojan (source also of Old High German laffen "to lick," Old Saxon lepil, Dutch lepel, German Löffel "spoon"), from PIE imitative base *lab- (source also of Greek laptein "to sip, lick," Latin lambere "to lick"), indicative of licking, lapping, smacking lips.

Of water, "splash gently, flow against" first recorded 1823, based on similarity of sound. Figurative use of lap (something) up "receive it eagerly" is by 1890. Related: Lapped; lapping. The noun meaning "liquid food; weak beverage" is from 1560s.
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lap (v.2)
early 14c., "to surround (something with something else)," from lap (n.1). Figurative use, "to envelop (in love, sin, desire, etc.)" is from mid-14c. Meaning "lay one part over another, lay in such a way as to cover part of something underneath" is from c. 1600. The sense of "to get a lap ahead (of a competitor) on a track" is from 1847, on notion of "overlapping" (see lap (n.2)). Related: Lapped; lapping.
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lap (n.2)
1670s, "something coiled or wrapped up," from lap (v.2). Meaning "part of one thing that lies on and covers another" is from 1800. Meaning "a turn around a track" in a distance race is from 1861. Related: laps.
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cat-lap (n.)

also catlap, "thin, poor beverage (especially weak tea)," 1785; see cat (n.) + lap (v.1). The notion is "fit only to give to cats."

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lapful (n.)
1610s, from lap (n.1) + -ful. In old slang, "a lover or husband," also "an unborn child."
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lappet (n.)
"a small flap," 1570s; earlier "lobe of a body part" (early 15c.), from Middle English lappe "lap" (see lap (n.1)) + -et, diminutive suffix.
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laptop 
also lap-top, in reference to a type of portable computer, 1983 (adjective and noun), from lap (n.1) + top (n.1), on model of desktop.
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lapel (n.)
part of a garment folded back and overlapping another, 1751 (implied in lapelled), from lap (n.2) + -el (2), diminutive suffix. Compare lappet.
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overlap (v.)

"to lap or fold over, to partially extend over, extend so as to rest or lie upon," 1726; see over- + lap (v.2). Verbal phrase lap over "extend beyond" is recorded from 1630s. Related: Overlapped; overlapping.

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