Can I keep on pumping Phyrexian Devourer?
Yes, you can achieve what you want by activating Phyrexian Devourer's second ability and Jarad, Golgari Lich Lord's second ability in response to Phyrexian Devourer's first ability.



Most abilities trigger when when an event occurs. This one is different.


  603.8. Some triggered abilities trigger when a game state (such as a player controlling no permanents of a particular card type) is true, rather than triggering when an event occurs. These abilities trigger as soon as the game state matches the condition. They’ll go onto the stack at the next available opportunity. These are called state triggers. (Note that state triggers aren’t the same as state-based actions.) A state-triggered ability doesn’t trigger again until the ability has resolved, has been countered, or has otherwise left the stack. Then, if the object with the ability is still in the same zone and the game state still matches its trigger condition, the ability will trigger again.
  Example: A permanent’s ability reads, “Whenever you have no cards in hand, draw a card.” If its controller plays the last card from his or her hand, the ability will trigger once and won’t trigger again until it has resolved. If its controller casts a spell that reads “Discard your hand, then draw that many cards,” the ability will trigger during the spell’s resolution because the player’s hand was momentarily empty.


Because Phyrexian Devourer's first ability won't go on stack as long as it's already on the stack, you can freely activate its second ability as many times as you want in response to its first ability.


Activate Phyrexian Devourer's second ability.
Let it resolve.


Phyrexian Devourer gains +1/+1 counters.

[...]
Activate Phyrexian Devourer's second ability.
Let it resolve.


Phyrexian Devourer gains +1/+1 counters.


Phyrexian Devourer's first ability triggers.


Place Phyrexian Devourer's first ability on the stack and retain priority.
Activate Phyrexian Devourer's second ability (in response to its first).
Let it resolve.


Phyrexian Devourer gains +1/+1 counters.

[...]
Activate Phyrexian Devourer's second ability (in response to its first).
Let it resolve.


Phyrexian Devourer gains +1/+1 counters.

[...]
Activate Jarad, Golgari Lich Lord second ability (in response to Phyrexian Devourer's first).
Let it resolve.


Jarad, Golgari Lich Lord causes your opponents to lose a bucktetload of life.

Let Phyrexian Devourer's first ability resolve.


It does nothing.