by 1989, also a verb; see lap (n.1) + dance (n.).
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]
In anatomy, lap is attested by late 14c. as "loose end or lobe of flesh" (as in dewlap) and from 15c.-17c. lap (often in plural) was a euphemism for "female pudendum." but this is likely not the immediate source of lap-dance.
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."