Peter Pan in Kensington Gardens by J. M. Barrie with drawings by Arthur Rackham, 1906
No, Peter Pan did not kill the lost boys originally. Peter Pan wasn't a fairy tale, he was a character in Peter Pan in Kensington Gardens as a completely different character with a different story who was then used in the play Peter Pan; or, the Boy Who Wouldn't Grow Up. The Lost Boys are sent to Neverland as babies and return to Earth when they grow up and get replaced by new Lost Boys. Hook wasn't a Lost Boy as it is implied in the play that he attended collage and came later to Neverland.