“With each level of this Perk, you gain an additional 4 Hit Points every time you advance a level. This is in addition to the Hit Points you already gain per level based off of your Endurance.”— Fallout 2 in-game description
Every time the player character gains a level, they gain an additional four Hit Points for each rank of this perk. With two ranks of Lifegiver, that's +8 HP each level, which is more than 10 points in Endurance would give you.
Lifegiver grants +4 HP for every level gained, including the level when the perk was taken. (Fallout Tactics does not give the HP on the level you take the perk.)