Multiple instances of lifelink are redundant, so giving lifelink to a Human that already has it gives no additional benefit.

Jerren's last ability will trigger only if you have exactly 13 life at the beginning of your end step. You will be able to pay only if you have exactly 13 life as that ability begins to resolve. If your life total isn't 13 at that point, the ability will have no effect. You won't be able to pay and Jerren won't transform.

If, while activating mana abilities during the resolution of Jerren's last ability, you somehow gain or lose life, you will still be able to finish paying the cost and Jerren will still transform.