The “mountainside” is in Chapter 4, so it’s not a different region or mountain range.  Everywhere else in the work, it is hyphenated.  In no instance does “mountain side” occur in the work.

• 04.002 Boulders, too, at times came galloping down the mountain-sides,
• 04.005 and shouting all over the mountainsides.
• 06.093 on a wide shelf of rock on the mountain-side.
• 11.011 or he might be lying out on the mountain-side keeping watch,
• 11.013 searching for paths up the mountain-side.
• 11.028 some were roving about the mountain-side.
• 11.038 in the mountain-side,
• 12.029 licking the mountain-sides with flame,
• 12.031 and round the mountain-sides.
• 12.032 and had scaled the mountain-side
• 12.067 Not much use on the mountain-side?
• 15.003 when Smaug smashed the mountain-side,

“Mountainside” has its own entry in OED, where it does appear hyphenated in the examples.

“mountainside, n.” OED Online, Oxford University Press, June 2017, http://www.oed.com/view/Entry/122907. Accessed 19 September 2017.