Chapter Five (1951) includes twenty-six hyphenated words, used thirty-two times.  Tolkien invented fourteen of them, used nineteen times, over half, either way you count. Thank you, internet, for being my lab notebook.

• back-door
• bat-wing*
• birthday-present
• blind-man’s-buff*
• blood-curdling
• door-post•
• drip-drip-dripping*
• egg-question*
• fish-bones*
• flip-flapping*
• four-legs*
• goblin-guards*
• goblin-wars*
• half-imagined*
• hiding-place
• lamp-like*
• no-legs*
• one-leg*
• out-of-doors*
• riddle-game*
• side-passages
• three-legs*
• to-do*
• tunnel-wall
• two-legs*

The asterisks indicate which words were also used in 1937. In Chapter five in that edition is also:

• good-bye [1937.05.096] and said good-bye to the nasty miserable creature;

I am fascinated that “birthday present” from 1937 gained a hyphen when it was re-envisioned in 1951.