Lebow, who has fought brain cancer to a standstill, got to know many of the children when he was receiving chemotherapy at the center.
He was Mayor when he received a new heart Feb. 18, 1987, at the medical center.
Clients can receive mail at the center, but no one dares give the address to potential employers.
The winner will receive a cash award of $5,000 and a solo exhibition at the center.
In other words more sealed boxes passed through the border than were received at the center.
The children have been invited to receive counseling at the center, but they have not yet accepted the invitation.
Thirteen babies have received new hearts at the center, with nine surviving.
He had been suffering from the ailment for two years and received a bone marrow transplant at the center in April 1995.
"It really, really touched a nerve," one rape victim who received counseling at the center this year said.
Almost 44,000 people received medical care at the center in 1968.