".How do you have low unemployment AND low labor participation without there being massive lying or distortion of real employment trends??"
All popularly reported and endlessly regurgitated "economic" measures and "indicators", are just simple, mindless, Newspeak.
It's not that they can't be well defined in a strict technical sense. But rather that the name chosen for them, intends to convey that they describe something meaningful in the real world. Which they don't.
They're popular because they are so simplified that they allow clear means for politicians, apparatchiks, bureaucrats, banksters and other busybodies to "manage" them in a supposedly "good" way. By the usual micromanagement and interference in the lives of others, that is all the above can ever hope to do. (In a Fiat regime, they are all, specifically, highly correlated with simple debt growth. To the point where there is no need to follow any of them. Just look at debt growth. If it's accelerating, every "indicator" show "the economy" doing "good." And vice versa. Nice way for pointless, useless banksters and their protector Saint The Fed to pretend they are somehow useful for anything at all...Which, of course, they aren't.)
Economics, as properly practiced (read Rothbard), pays no attention to any such metric. As none of them mean anything. There simply exists no little tweaks and levers by which a bunch of clueless apparatchiks can "manage" "the economy" to make it "better." All such "management" does, per definition, is gum up the works of a system that; always, everywhere and for all of history past, current and future, on any possible planet and in any universe aside from possibly Heaven; works best if the apparatchiks were all dead and replaced by noone.
Which, of course, isn't what the of-less-use-alive-than-dead crowd wants to hear. So they instead make up pointless, meaningless "indicators" of what they insist are measures of "the people's" wealth and "well being." Which they can then busy themselves screwing and messing around with at will. Hoping none of the actual "people" notices, that despite "the economy" supposedly doing so "well," people themselves are, in fact, having less and less in common with free and reasonably well off citizens; and instead are looking more and more like simple indentured servants. And subjects of a childish, progressive social experiment that, even in theory, has an exactly, identity, zero chance of ever ending well.