middle school vs lyceum

middle school and lyceum both are nouns.

Word	Noun	Adjective	Verb	Adverb
middle school	Yes	No	No	No
lyceum	Yes	No	No	No

As nouns, middle school and lyceum are synonyms defined as:

middle school and lyceum: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other synonyms of middle school include Gymnasium, lycee, secondary school.

middle school (noun)	lyceum (noun)
a school for students intermediate between elementary school and college; usually grades 9 to 12	a public hall for lectures and concerts
	a school for students intermediate between elementary school and college; usually grades 9 to 12