In the episode "There Will be Blood", Lorelei tracks down the people she believes to be behind her sister's abduction and murder, and exacts revenge. The second culprit (Jason) admits to being an accomplice of Red John, confirming that it was actually Red John who killed her sister.
After her worst fear comes true, Jane asks Lorelei to give up Red John's real identity, as was their deal. Lorelei in turn refuses to do so and asks Jane to get that name from Jason. She says something along the lines
Hes weak! He'll give him up.
and later shoots Jason.
I fail to get her motivation to kill Jason there? Moreover, after she has shot Jason, there is no emotional outburst on Jane's part. Shouldn't he go berserk now that Lorelei has refused to give him Red John and also shot his solid lead?