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 verb in The Etymologies of the 1930s glossed “to stray” appearing in its Noldorin-style infinitive form rhenio under the root ᴹ√RAN “wander, stray” (Ety/RAN). In the entry for ᴹ√RAM it was glossed “wander”, along with a homonym N. rhenio⁽⁾ “fly, sail” derived from ᴹ✶ramya-. The two verbs collided because ancient my became ny in Noldorin/Sindarin.
Neo-Sindarin: Many Neo-Sindarin writers adapt this verb as ᴺS. renia- “to stray, wander” 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.