lefthander vs left hander

lefthander and left hander both are nouns.

Word	Noun	Adjective	Verb	Adverb
lefthander	Yes	No	No	No
left hander	Yes	No	No	No

As nouns, lefthander and left hander are synonyms defined as:

lefthander and left hander: a baseball pitcher who throws the ball with the left hand

Other synonyms of lefthander include left-handed pitcher, left-hander, lefty, southpaw.

lefthander (noun)	left hander (noun)
a baseball pitcher who throws the ball with the left hand	a baseball pitcher who throws the ball with the left hand