Leon didn't go to his apartment or anywhere near that direction. He didn't want to take any unnecessary risk that could give out his identity as Leon.
However, Leon was injured from the shot, and he could barely run fast.
Of course, he wasn't feeling any pain, but his blood kept bleeding.
"Why… isn't it healing?" Leon wondered as he stopped in an alley to catch his breath.
"It should start healing… So why…"
It wasn't as though his wound wasn't healing. It was healing but at a slow speed.
He was shot on his lower back on the spinal cord, yet he was still able to jump and run for a while. Since he couldn't feel any pain, Leon hadn't realized that his wound was more fatal than he thought. The shot would have killed any other ordinary human, but Leon's superpowers saved him. Although, not for long.
If he had stayed a little longer or tried to kill Mr.L, Leon wouldn't be able to escape.