Life Absorbing Machine
Type: Continuous Trap
Effect: Each time you pay Life Points, you gain half of what you payed back during your Standby Phase.
Not the exact text, but that's the basic point. And paying is not like battle damage, but:
Player A pays 2000 Life Points for IFL
Player B ends Turn
Player A draws, goes to standby phase, gains 1000 Life Points back from LAM