• 05.012 He was looking out of his pale lamp-like eyes for blind fish,

This word is attested in OED with a reference I’m certain that Tolkien knew:

a1822   Shelley Cyclops in Posthumous Poems (1824) 356   Fire will burn his lamp-like eyes.

“lamp, n.1.” OED Online, Oxford University Press, June 2017, http://www.oed.com/view/Entry/105340. Accessed 14 September 2017.