left hander vs lefthander

left hander and lefthander both are nouns.

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

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

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

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

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