Do Triggered effects stack?
You get four lifes in total: one when each of the four triggered abilities resolves.

Since you have four copies of Suture Priest on the battlefield, you have four copies of the triggered ability. Each time the event a triggered ability is indicating happens, it triggers. Since you have four copies, it trigger four times.


  603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers.


Since there is no rule that stops several copies of the same triggered ability to trigger at the same time, they all work.