secondary school vs lyceum

secondary school and lyceum both are nouns.

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

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

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

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

secondary 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