I've been a Clippers fan for years, and I'm not naive enough to say that they'll overshadow the Lakers one of these days. However, Los Angeles isn't exactly a place like Pittsburgh, Chicago, or Detroit where they ride or die with their teams. Each of the local teams here (both in Los Angeles and Orange Counties) are have their sets of hardcore fans, but the bandwagoners swell up once these teams start winning.
The Clippers, in fact, were all set to move to Anaheim permanently in '99 if not for one of Donald Sterling's real estate buddies stepping in and brokering a deal with the owners of Staples Center (the same people who own the hockey Kings and 25% of the Lakers). The Clips pay just over $1 million a year for their lease at Staples, and get to keep all revenue generated for each home. That reason alone is why that as long as Sterling owns the team, they'll stay being roommates. I never liked the fact the Clippers and Lakers share the same arena; never mind the fact the Lakers are more popular, but because of scheduling priority...the Clips just completed a 11-game road trip during February, thanks to the Grammys and the NBA All-Star occupying Staples. During that same time frame, the Lakers had a seven-game trip out of town.
There are other venues in Los Angeles County alone that the Clippers could take up residence (such as the old Forum), but they would need a massive renovation to make it happen. I know Sterling won't foot the bill, and there's no public money available.