Lisa has some good advice. One other suggestion is to put a small hand mirror inside a cage so that the bird comes inside to check out the "other bird" .

You can also try to report the bird on 911 parrot Alert:
http://www.911parrotalert.com/FoundBirdReport.html

Also check Craig's List, the local vets office, etc to see if anyone has reported the missing bird. As a bird owner, there is nothing worse than to have one of them fly away, never to be found again. Of course, there are idiots who think that a domesticated parrot can survive in the wild, and set them free to meet a violent death or starvation.

This lovebird might be OK for awhile, but chances are not good that it would survive any cold weather. Feral quakers have adapted over time to the climate in New York and other cold-weather cities.

Good luck!