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 your character gains a level, you 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.
Although it's not clear from the description, Lifegiver grants +4 HP for every level gained, including the level when the perk was taken.