A children's riddle asks what everybody has when they're sitting that nobody has when they stand. "Lap" may mean a person's front when he's sitting. "Lap" may also mean a tour about a racetrack or other circuit, or be short for the "overlap" of two pieces of material. Most strangely, "lap" may also be how a cat drinks water. Before you look anything up, you might guess that the animal drinking "lap" might be onomatopoeic--that the word simply imitates the sound a big dog makes slobbering up water.
A good etymological dictionary opens a wonderland of history. First, the "lap" which is a person's seated front is the source of many of the other senses of the word, including the idea of enfolding or "overlapping" which is mildly archaic in many of its meanings ('lap pie crust over the filling' or 'lapped in sables'). The circuit of a racetrack is the same idea. But the "lap" of an animal drinking is extraordinary. The two words have been homonyms since Middle English, lappen. Only earlier were are the words distinguishable by sound or appearance. Once we get back as far as Old English, the 'slurp' is lapian while the seated front is læppa, the flap of a garment.
As frequently happens, the most archaic sense of a word is its oldest. The hanging flap of a garment is a very old sense of the word "lap" that we now sometimes attach to part of the person behind the garment.
Going back further yields more surprises. The drinking "lap" is most unusual, since only two other words can be traced to the same Indo-European root. The IE root is *lab-, believed to mean smacking the lips, licking. Our present "lap" thus carries the central idea of the original word forward with great fidelity. Slightly nasalized, the root went into ancient Germanic as *lamp-, to drink, surfacing again in Old French as lamper, to guzzle. In 17th century France, a common refrain of popular poetry (and songs?) was lampons, or 'let us drink.' This gives a vivid picture of what 17th century French poetry must have been like. English gets "lampoon" from this source. You can be confident that "popular" poetry in the ale-houses was a roughly humorous breed of entertainment that caricatured (or "lampooned") the famous of the day.
The fact that Old French adopted a Germanic word for drinking and gave it an intense meaning, 'to gulp down,' also suggests to me that along the marches where the elder proto-French and the proto-Germans met, the Germans were considered the more heroic drinkers.(1) (I'm assuming here that the early French had to adopt the word from their neighboring Germans, even though the French themselves were originally the Franks, a Germanic stock. For some reason, they retained practically none of their original laguage when they adopted the debased Latin that eventually became French.)
The only other English word which is cousin to "lap" (to drink) is "lambent." The trace here is to Latin lambere, 'to lick.' Hence "lambent" really means a flickering, which we have come to associate with light, as a flickering ("lambent") fire. In modern usage, "lambent" may mean as little as "luminous," with no sense of twinkling at all.
Thus "lap," despite its Indo-European heritage giving rise to Latin and Germanic kin, has in English only the two distant relatives "lampoon" and "lambent" which, I dare say, would not be recognized as family members at all without benefit of this little history.
But what, I hear you asking, about similar appearing words which have somewhat overlapping meanings. "Lamp," for instance, looks and feels like it ought to be related to "lambent," if we hadn't just learned that lambent meant licking, not luminous. As it happens, this is just a chance resemblance; "lamp" derives from middle english, from old french, from Latin lampas, from Greek, where it was formed from a verb meaning to shine. The IE root is *lap-, to shine or burn.
1 What the Germans were likely drinking so heroically was ale or beer, which is itself a word related to more generalized drinking words, like beverage, imbibe. The IE root is *po(i)-, which also gives us potion, potable and symposium (literally, "drinking together"). It might seem curious that the Germans had to borrow a generic word for beverage from the Romans and apply it to mean beer, perhaps their most common drink. In fairness, though, the more common word for our daily tipple was "ale" until about the sixteenth century. It is ale that was the German favorite in ancient times (as Tacitus tells us), and "ale" seems to stem from an IE root *alu-, having something to do with magic or intoxication, and also giving us (perhaps) "hallucinate."