As the site's foremost Westbrook defender, I am happy with the trade. The worst case scenario for me in any season is that the Lakers win the championship. If they win next year I will at least be consoled by Westbrook being a part of the team.
Westbrook simultaneously solves some of the Lakers problems while exacerbating others. One of the key issues for the Laker's last season was that they didn't have another natural creator besides LeBron. This was a major problem for them offensively during moments when LeBron sat or was injured or not 100%. Davis, for all of his talents, is not a natural creator and though he can score, it becomes difficult for him facing double-teams and having to make quick decisions to get limited players good shots. Westbrook in theory solves that issue, because he is a natural creator that can get other players good shots, both in the half-court and transition.
The problems for the Lakers come from all of Westbrook's faults, few of which can be easily hidden on this Lakers team. The first is that he is a lazy/bad defender who always guards the opponent's weaker player. LeBron usually takes that role because he wants to conserve energy. While both guys are capable of being good defenders thanks to their athletic superiority, it becomes a challenge when two of your best players are bad defenders who don't want to try hard on that end for most games.
The second issue is a lack of shooting; LeBron is an okay shooter, as is Davis, but teams will gladly pack the paint and let them shoot. Westbrook is an abysmal three point shooter, so now you aren't getting good shooting from 3 positions on the floor. So you need to get pretty good shooters to fill out the rest of the roster. You also need to get good defenders to fill out the rest of the roster to make up for the Westbrook/LeBron issue on that end of the floor. Can you find that many good 3&D guys in the bargain bin?
The third issue is that Westbrook to be at his best, needs to play in a transition-oriented offense. Westbrook can create his own fast breaks thanks to his incredible defensive rebounding and ability to push the ball down the court. This is also when his best playmaking skills are on display as he will gladly feed his teammates for easy buckets if they run the floor with him. But who will run the floor with him? The Lakers shipping out a lot of their younger role players hurts because those are guys who would run the floor with Westbrook. LeBron, for all of his gifts as a transition finisher, isn't doing that as much anymore. If you bring in savvy vets, you aren't getting the same energy and you need some young energy guys to run with Westbrook. One of the reasons he thrived in the second-half of last season in Washington is that he was playing with a lot of hungry young players looking to make it in the league, and they were eager to get out and run.
The final issue is health. While Westbrook has maintained an impressive energy level throughout his career, he hasn't always been healthy, and with his playing style, age, and odometer, he is a real injury risk. LeBron has had two recent seasons derailed by injuries and isn't getting any younger. Davis has had issues staying healthy his entire career. This is a pretty high-risk team and its a real question mark who is going to be 100% next spring.