"of or pertaining to the side," early 15c., from Old French latéral (14c.) and directly from Latin lateralis "belonging to the side," from latus (genitive lateris) "the side, flank of humans or animals, lateral surface," a word of uncertain origin. Specific sense "situated on either side of the median vertical longitudinal plane of the body" [Century Dictionary] is from 1722.
As a noun, from 1630s, "a side part;" as a type of pass to the side in U.S. football, it is attested from 1934 (short for lateral pass). Related: Laterally.
-ity
word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).
Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]