It'd take a lot for the Clippers to overtake the Lakers locally. A few years back, I went to a Staples Center doubleheader with the Clippers/Cavaliers and Lakers/Knicks (plus the Devils/Kings the night before). I expected there to be much more buzz for the first game since it was the height of the Chris Paul / Blake Griffin era and LeBron was in town. Meanwhile the Lakers were last in the Western Conference. But it was completely the opposite to my surprise. Also seemingly a lot of tourists as well as the Lakers are a name brand.
It'd take a (short) generation of new fans for the Clippers to wash off the stink of the Donald Sterling era. They were a gong show / punching bag locally for so many years. Unless the Clippers went on a dynasty run and the Lakers turned into the Dolan Knicks, I wouldn't foresee it happening any time soon.