h₁lewdʰ-
“people, to grow”people, folk, free
Root for people/growth, yielding German Leute (people), Old English leod, Latin liber (free).
Discussion
The PIE root *h₁lewdʰ- (to grow, to rise — extended to "people, the growing ones") produced vocabulary for human communities and demographic growth across the Germanic and other branches.
Old English lēod (people, nation) and the related lēode (people, subjects) continue the root natively. The word is archaic in modern English but survives in German Leute (people) — one of the most common German words for human beings collectively. The Gothic liudan (to grow) preserves the original verbal sense.
The root may also underlie the English word loud (OE hlūd, from PGmc *hlūdaz — "heard, famous" — from the concept of growing/rising in sound), though this connection is debated.
Latin līber (free — originally "belonging to the people," a free person as opposed to a slave) may derive from a related form, though many scholars treat it as a separate root. If connected, the word free in the PIE world was defined by membership in the community: to be free was to belong to the *h₁lewdʰ-, the growing people.
Greek eleútheros (ἐλεύθερος, "free") is sometimes connected through a similar chain: the free person as the one who belongs to the folk, who has grown up among the people. The English word liberal (from Latin līberālis, "pertaining to a free person") and liberty would then ultimately trace to the PIE concept of communal belonging.
The root's semantic core — growth that produces community — encodes a collectivist vision of social identity: people are "the growing ones," defined not individually but as a collective that increases. The community IS its growth.
Notes
Pokorny 684-685. English liberal from Latin liber (free person).