Lethal Weapon season 2 will see Trish getting a new job, but Murtaugh will not be so happy about what it entails. That said, expect to see the couple going through some marital issues as they deal with new challenges.
Check out this preview on what to expect, per EP Matt Miller:
What happens is that she starts working later and she starts traveling, and maybe he doesn't quite reciprocate that as much. He becomes a little bit more insecure and possessive and that starts to cause friction in their marriage.
You get fun later on in the season with Murtaugh having marital trouble and going to Riggs, and Riggs being like, "Yeah, I'm not interested in talking about that." Whereas Riggs, anything he wanted to talk about, [Murtaugh] was always there for him, so we realize Riggs isn't quite that same friend in the same way.
BONUS SPOILER BIT:
* Miller on what to expect from Hilarie Burton's return as Palmer:
What happens is when Riggs starts to feel like he's putting Miranda behind him and he's healthy and normal, he does all the things that a healthy person would do. He gets up and he tries to exercise and clean his trailer... but he doesn't understand how to be normal. Part of his idea of what it means to be normal is to start dating again, so he takes a case that has a very thin connection to drugs and starts to think that there may be a DEA component in this. So he brings [Karen] (Hilarie Burton) into a case when there's really no reason for her to be in the case.
When he goes to her, he realizes she's been sort of relegated to the basement of the DEA because of her having assisted him at the end of Season 1. So he wants to win her back romantically, but then he also wants to help her career also, which he was kind of responsible for messing up.
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