The reason Beric resurrected Cat was that he had promised Arya to reunite her with her mother, and obviously because he was kind of tired with unlife. Another observation. As far as we can tell, Beric's and Cat's faculties, other than memory in Beric's case, seem intact. On a possible trial be combat.Lady Catelyn has no reason to give Jaime a trial by combat. Trials are meant to determine guilt or innocense. She knows he is guilty, at least of pushing Bran out the window. She also knows of his actions at the siege of Riverrun. She can hang him for these. The only thing that is in question is whether she charged Brienne with finding Sansa in order to keep her safe or to deliver them to the queen. For that she might make Brienne find him. This would be a very interesting trial. For one Jamie does not need to be alive for Brienne to keep her oath to him. Also, A victorious Brienne would mean that they are both guilty.