I think to work, it would have to be something more like this:
Utah:
Out Mitchell (to NYK), Beasley (to LAL)
In Westbrook, Picks, Picks, Picks....
LAL:
Out Westbrook and Picks (to UTA)
In Beasley, Rose, Fournier
NYK:
Out Rose + Fournier (LAL), Picks, Picks, Picks (to NYK)
In Mitchell
The issue is that NYK cannot take in Mitchell without sending out comparable salary. That is why Rose and Fournier need to go to LAL. And it makes sense for LAL to take these players. I would expect that NKY would provide the majority of the picks. Utah only needs to send out one player in addition to Mitchell to match Westbrook, they can do two as well and it still works, depending on exactly which two. I just picked Beasley as he made some sense for the Lakers. For example sending both Bogdanovich and Clarkson was too much for the Lakers to take back (assuming they have to take Rose and Fournier). Beasley can't be traded with other players until Aug 30. I think the report may have mixed up that it is 2 to the Lakers from NYK and only one from UTA to the Lakers.
This actually makes some sense for all teams. I am a little surprised that UTA would take Westbrook but if it gets them more picks, I guess that is their goal. I think this works for all teams.