Yes, LATE is a Scrabble word!

Letter values in Scrabble US: L 1, A 1, T 1, E 1.

Is it a valid word?

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

being or occurring at an advanced period of time or after a usual or expected time
after the expected or usual time; delayed
of the immediate past or just previous to the present time
having died recently
of a later stage in the development of a language or literature; used especially of dead languages
at or toward an end or late period or stage of development
(used especially of persons) of the immediate past

Also: of late.