Yes, LIMELIGHTS is a Scrabble word!

Letter values in Scrabble US: L 1, I 1, M 3, E 1, L 1, I 1, G 2, H 4, T 1, S 1.

Is it a valid word?

LIMELIGHTS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a focus of public attention
a lamp consisting of a flame directed at a cylinder of lime with a lens to concentrate the light; formerly used for stage lighting

Also: public eye, calcium light.