Lucius derives from Latin word Lux (gen. lucis), meaning “ light “ (< PIE *leuk- “brightness”, Latin verb lucere “to shine”), and is a cognate of the name Lucas. Another etymology proposed is a derivation from Etruscan Lauchum (or Lauchme) meaning “ king “, which however was transferred into Latin as Lucumo.
Lucius - Wikipedia
en.wikipedia.org/wiki/Lucius
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Not facts.
Thanks for the ety but I knew that.