In a word, it's eating pussy, by a male or female partner. Seeing as how most chicks these days trim the hedge, it's much more likely to be nappy than bushy downtown. Hence, you lap (lick) the nap.
1: A nap taken after blackout drinking; when you wake up it's night time 2: A nap taken after day drinking with friends; when you wake up it's night time
1: After I got roofied I took The Dark Nap
2: Down in Savannah we got drunk by 3pm and then took The Dark Nap