The life trap spell is given by the old woman hidden on colossus boulevard by Mindy PixieCrown. She is on of the "Secret Trainers" around the spiral. You might look and see if she has anything for any of your other wizards.
I do not understand why that trap is the only one that is separate from the school.
Life Trap is actually a secret spell. Life Wizards don't ever learn it. To get it you have to find the secret school in Collosus Boulevard. To find it, go down to the place where Mindy Pixiecrown is. Look to left, and there are some stairs down into a house. Go into the house, and there is a trainer that you can learn these spells from: Quench, Melt, Dissipate, Reshuffle, and Life Trap. :D