A Line Lead Mechanic realizes after their A320 aircraft had departed; he had given a Mechanic a left inboard Landing Light assembly to install that was not 'Effective' for the aircraft. Trying to make sure the flight left on time; he failed to notice the Landing Light Part Numbers (P/N) did not match.

Narrative

I was the Lead Mechanic [working] outside on an A320 aircraft which needed a left inboard landing light assembly that was found on a walk-around by the Flight crew. Another Lead Mechanic ordered the part and a Mechanic changed the part. To help with a on-time departure; I accomplished the [Maintenance] paperwork and entered the information into the Logbook. After the aircraft had departed; we found the aircraft 'Effectivity' was for a different series A320 aircraft.Prior to entering the information into the computer I was checking Serial Number (S/N) information and found that the Part Number (P/N) installed did not match the removed Part Number that had been installed. The wrong part was ordered and I did not double-check and verify that the part was correct. Time was also a factor; trying to make sure that the aircraft left on time. I also relied on my co-workers to order and install the correct part. Notified Maintenance Control; the Supervisor On Duty and spoke with the other Lead Mechanic and Mechanic that were involved. Maintenance Control reported that they would put [light assembly] on another flight. Prior to the aircraft leaving; all paper work should be completed. Double-check the aircraft effectivity; slow down and don't be in such a rush to release the plane.