lower court vs judicature

lower court and judicature both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower court	Yes	No	No	No
judicature	Yes	No	No	No

As nouns, judicature is a hypernym of lower court; that is, judicature is a word with a broader meaning than lower court:

lower court: any court whose decisions can be appealed to a higher court
judicature: an assembly (including one or more judges) to conduct judicial business

Other hypernyms of lower court include court, tribunal.

lower court (noun)	judicature (noun)
any court whose decisions can be appealed to a higher court	the act of meting out justice according to the law
	the position of judge
	the system of law courts that administer justice and constitute the judicial branch of government
	an assembly (including one or more judges) to conduct judicial business