Defense
First of all, I’m not expecting Metta to suddenly step into the center position and dominate seven-footers, but I do expect him to receive a significant amount of time at the power forward position.
His strength and physicality allow him to compete with many power forwards, and his quick hands are something many players at that position simply aren’t used to.
Similarly, the league prefers to play more “small ball” than it did about ten years ago, and with the Lakers now forced to play that style as well, opposing “undersized” teams are likely licking their chops at the fact of having no true big man to go up against when facing the Lakers–which has been bothersome for teams in the recent past. 
Teams like the Miami Heat and Oklahoma City Thunder will be sure to place their respective superstars–LeBron James and Kevin Durant–at the four slot and not have to worry about a big man in the middle if Dwight Howard misses more time with due to his injury or in instances where he’s off the court.
Even with Howard’s return, World Peace will still have to guard some of those stars down low, as well as the more traditional power forwards–along with Earl Clark and Antawn Jamison.
Antawn Jamison isn’t a great position defender, and while Earl Clark has played exceptionally well all around, Metta World Peace is still one of the better defenders in the league when he wants to be, and will have to take on the challenge of stopping bigger players. His defense of small forwards will be needed as well when Dwight Howard returns, as the team will still be without one seven-footer, and Howard will not be at 100 percent for the rest of the season.
Additionally, Metta is a capable rebounder who is currently pulling down an average of 5.7 boards this season. He’ll need to continue to rebound the ball well going forward as well.
The other two forwards (Jamison and Clark) have proven they can rebound the ball exceptionally well too, however, and must continue to do so.
Offense
Although Jamison and Clark have performed quite well, it’s up to Metta World Peace to set a tone offensively in the front court.
Kobe will likely have to shoulder a larger role offensively, as will Steve Nash, but World Peace is a proven scorer and his ability to score will be much needed.
Similarly, just as he’ll have to match up with bigger forwards on defense, he’ll have to do the same on offense. That’s not necessarily a bad thing as although his shot has looked solid at times this season and he’s often left open on the perimeter, he can be effective in the post as well.
I’m not expecting him to post-up and dunk on centers or anything, but he does possess a solid post game and if the Lakers proved anything over the past seven games, it’s that a strong post presence is necessary for the team to succeed.
Additionally, World Peace–despite averaging just 1.5 assists this season–can be a decent facilitator. He’s been focused on scoring at the offensive end much of this season, but for this team to be successful, they’ll need to collectively make up for some of the passing and play-making that Gasol had provided before going down.
I believe Metta World Peace has the capability to at least compensate for some of that.
Also, as exhibited in that four-game stretch, Earl Clark may be a candidate for distributing as well, as he averaged 3.5 assists–which is right around Gasol’s season average.
Leadership
Many many view World Peace as more of a loose cannon than a leader, but he truly is an emotional leader of this team. 
Nobody–besides Kobe Bryant–gets as fired up as World Peace does, and he’ll have to channel some of that passion into inspiring his team to play tough and win ballgames.
I know it seems kind of weird to refer to World Peace as a leader after he’s coming off yet another league suspension, but it’s true.
World Peace is one guy on this team who Kobe Bryant trusts to always give it 100 percent out on the court, and he’s the only player remaining in the lineup that he’s won a championship with.
Metta has been a leader on plenty of teams in the past, and will have to lead by example as well as encourage some of the younger guys (yeah, there’s a couple younger guys on the team). Although the onus to step up will essentially fall on the team as a whole–especially on Dwight Howard and the three remaining forwards–at this point in the season and with a depleted front line, World Peace may just be the Lakers’ X-Factor.