A single engine pilot reported a loss of control while attempting to land. The aircraft drifted left of center and while airborne made contact with some runway lights. With help from the accompanying CFI; a go-around was accomplished and then a normal landing.

Narrative

I was flying Aircraft X for the first time on a training flight from ZZZ to ZZZ1; with a CFII on board. The flight to ZZZ1 was uneventful. When on short final; around XA:45 hours; I saw that I was a little low; and a little slow; and needed to get beyond the displaced threshold so power was added. I got past the threshold; but also ended up being left of center. I flared too high; and when the plane touched down it bounced. In not wanting to risk a hard bounce again; I applied full power to execute a go-around. The p-factor yawed the plane to the left; and pushed the plane even closer to the runway edge lights; while still trying to fly. The plane ended up being in line with the runway edge lights; and 2 or 3 were struck. At some point during this sequence of events; after the bounce and after the application of full power; my CFII took control of the airplane. After the collisions; the plane was landed under control; and on the runway. The plane never left the asphalt part of the runway. [Requested for priority] and we taxied to the transient parking and shut down without issue. Within the hour; after all of the appropriate notifications were made; my CFII and I did an analytical debrief of what transpired. As this was my first time flying this high performance plane; we discussed how much more the p-factor can affect the airplane. We talked about how the go-around decision was a good decision; but being left of center; then the input of full power and not being used to the new p-factor; all lined up to push us towards the lights. We also talked about power settings and had we not flared too high; and bounced; being left of center probably wouldn't have been an issue. It was a good debrief and I learned a lot. It also further reinforced making sure all things are set; and the pilot and plane are set up for success on landing. Training with this CFII will continue; as will the adage of having a pilot's license is a license to learn. Thank you for your time.