The Etymologies of the 1930s had N. {rhein >>} rhain “free” derived from ᴹ✶(a)ranı̯ā under the root ᴹ√RAN “wander, stray”; it also had a deleted variant erein, presumably from aranı̯ā (EtyAC/RAN). See also S. rain “erratic wandering” for a later appearance of a similarly derived word.
Neo-Sindarin: Many Neo-Sindarin writers adapt this adjective as ᴺS. rain “free” for purposes of Neo-Sindarin, as suggested in HSD (HSD), since the unvoicing of initial r to rh was a feature of Noldorin of the 1930s but not Sindarin of the 1950s and 60s. I would use it as “free” in the sense “✱unconstrained”.
A variant of the verb N. lheithia- “release, set free” from The Etymologies of the 1930s, a combination of that verb with the prefix ad- “again”, so more literally “✱to free again, re-release” (EtyAC/LEK). It also had an archaic basic verb form N. †adleg- and a noun form N. adleithian. None of the ad-prefixed variants appeared anywhere else.