Amy's "award" for winning would be a bone marrow donor for her brother.
If Lucas was a match to her brother, then her killing him would save him.
On the other hand, Lucas was playing for someone too, and suppose Amy was a match for his loved one.
Dr. Barden played with loaded dice, it was always meant to come down to those two.
Iris, not Amy. My mistake.
shareA living person can be a bone marrow donor. Remember earlier in the movie it was discovered that Iris herself wasn't a good match--generally, siblings are good matches because they have similar genetic codes. So, if Lucas were a match, killing him wouldn't have helped.
Now, if Lucas's sister needed a heart transplant, and Iris were a match, then shooting her in the head might work (but they'd have to get her body to the hospital for the transplant ASAP).