This is a familiar scene, in which parents keep silent, lest the children hear. Had they spoken Lilliputian amongst them, they could converse freely, without ever worrying about the children.
Artist: Louis Le Nain (1593-1648)
Irving Rothman, a Professor of English at the University of Houston claims that the Lilliputian language stems from Hebrew.
Researching this even further, I can confirm that the Lilliputians are descendants of one of the 10 lost Jewish tribes, expelled from Israel in 733 bc. The tribe of Naftali, sea-farers who inhibited the shores of the lake of Galilee, found their way to a remote island, and called it Naftalilliput. With the passage of time only the name Lilliput survived.
Another theory is that the Lilliputians are possibly descendants of earliest "mythical" creature in all of Jewish lore: Lillith. She was rumoured to have been Adam's first "mate", before Eve, who was a mate more like unto himself. Lilith is said to have abandoned Adam to return to the wilds and live among the animals and night beings.
"Put Yan" literally means a small genital (or "little fucker".) So it is plausible that given the ancient Hebrew nuances that pervade their language, "Lilith Put Yans" slowly eroded to "Lilliputian" over the aeons.
Here you can learn Lilliputian, as well as Lilliputian etymology.