The ability triggers just once for each life-gaining event, whether it’s 1 life from Soulmender or 8 life from Meditation Puzzle.

If you gain life at the same time Wall of Limbs is dealt lethal damage (probably because you control a blocking creature with lifelink), Wall of Limbs’s triggered ability will trigger, but Wall of Limbs will be destroyed before the ability resolves.

Use Wall of Limbs’s power as it last existed on the battlefield, including any +1/+1 counters it had, to determine the value of X.