DA-42 instructor pilot reported landing safely with the landing gear up when the left main gear failed to extend.

Narrative

I am writing a statement about the incident that happened at ZZZ in Aircraft X. It was a normal commercial multi training flight with my student; and my second flight of the day. We departed ZZZ and went out to the east. We did maneuvers then went to ZZZ1; and completed three landings: 2 touch and gos and one full stop. We then proceeded to ZZZ for a full stop landing. Once we arrived midfield left downwind runway XX; my student put the gear down where the right main light came on; the nose wheel light came on; but the left main gear light did not. We tested the gear warning button and all the lights were operating; I took over flight controls and asked for a low approach to see if my gear was down. Tower and another aircraft confirmed the left main was not down. I requested priority with ATC.I departed back to the east to troubleshoot and run through the checklist. After the emergency gear extension did not deploy the left main landing gear; we proceeded to do a series of high g maneuvers to see if the gear would fall free. After multiple attempts running the checklist and trying high and low speed gear extension; I proceeded to go back to ZZZ and did one low approach with the gear up to practice my approach. I came back to land runway XY with my gear up. I decided landing with the gear up was the safest option for me and my student. Once after a successful and safe landing my student and I evacuated the aircraft.