Lower courts in the american system include

state courts

Explanation:

lower courts are courts that are mainly used to entertain smaller charges examples of such courts are Magistrate courts. the smaller courts take up cases which are comprised mainly of civil charges other than criminal charges. capital offense charges are entertained at higher courts which are Federal courts like the Federal high court, Appeal court of justice and the supreme court of justice.

The lower courts as seen in Magistrate court is been presided over by a Magistrate and its Jurisdiction is usually restricted within the state, cases that are Federal cases are not judged in lower courts because they are mainly state courts and lack Jurisdiction to pass a Judgement on such cases.

i don't know why don't you google it?