Mechanic reported attempting to pass a logbook to flight crew through the flight deck window using a lift. The lift rolled backwards into the aircraft and the mechanic jumped from the lift.

Narrative

I was sent to Gate XX to Aircraft X by my Lead so the original pilot can fix his write up on Aircraft X log book. When I got to the gate the aircraft was already push back on the aisle way. I used the ramp headset and spoke to the Pilot. Who I was and why I was there. I ask him if it was ok for me to bring a lift & give him the log book through the window so he can fix his write up. He said ok. I ask him to turn his engine #1 off & he gave me a signal to come through engine #2 to double check I ask him again to turn his engine #1 off. he gave me the signal to come around engine #2 for the second time. I said ok; few minutes later I drove across in the front of the Aircraft X and park the lift on the right side of the aircraft under co pilot window. When I came back the ramp people were gone but the engine #2 was off. Since engine #2 was off I thought me and the Pilot were on] the same page. I park the lift and put the stabilizer down before I can go up the aircraft started rolling but engine #2 was still off. Try to move it but there was nothing I can do so I jumped off the lift. After that the aircraft impacted the lift.I was rushing and didn't follow all the steps. [I should have taken my] time.