Damn, I really don't see the Kings as a good fit but let me give it a go...
Kings have a surplus of RHD and youth which they would want to be the focal point. I think something along the lines of a roster Dman, a roster forward or youth forward with upside and a draft pick/prospect is a likely offer from LAK. I'll list some pieces that could be available, listing them in groups from more to less valuable. Pick one from each category, and obviously the higher one players form a category is, the more likely LAK would push for a lower tier player/asset in another category.
Roster Dman:
Sean Durzi (RHD, RFA, previous salary about 800kAAV, 23yo)
Matt Roy (RHD, 2x years left at 3.15AAV, 27yo)
Scott Walker (RHD, 2x years left at 2.65AAV, 27yo)
Roster or youth forward with upside ready to step into an NHL lineup:
Alex Iafollo (LHW, 3x years left at 4AAV, 28yo)
Gabriel Vilardi (RHC/W, RFA, previous salary almost 900k, 22yo)
Rasmus Kupari (RHW/C, 1x year left around 865k, 22yo)
Lias Andersson (LHW/C, RFA, previous salary about 875k, 23yo)
Jaret Anderson-Dolan (LHW/C, RFA, previous contract about 750k, 22yo)
Prospects/picks:
We've got plenty of both, take a look for yourself
I think LAK would love to move Scott Walker as he's been rather out-of-sight-out-of-mind, and with the emergence of Sean Durzi he's likely been pushed out or will be forced to play on the left side if returning to LAK (which he's done a decent job of in the past). His two injuries have been freak occurrences (crazy hard slapshot to the face, someone falling on his knee sideways) so I wouldn't call him injury prone, but clearly he hasn't played much in the last 2 years.
My offer (hopefully not too embarrassingly off... I'd love to see PHI fan's counter offers):
Walker + Vilardi + LAK 1st round pick