lyceum vs middle school

lyceum and middle school both are nouns.

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

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

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

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

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