The personal problem that Milton examined in his poem Lycidas is how to deal with the loss of loved ones.
He wrote in that poem about his best friend who died, so it is a sort of a manual on how to get over your grief as well. It is an ode to his best friend whom he lost and couldn't forget, so he decided to commemorate him in a poem and thus he will live forever through art.
Answer:
I think that the reason for Rainsford's change is because in the beginning is that he showed no care for the animals that he hunts. And now he shows remorse.