Just do what we used to do back in the good old days when we used to crush the Democrats....win the burbs and win the race.
The GOP problems really began in 1986 when many Los Angeles Republicans lost reelection. The trend away from the GOP is cleary evident when comparing CA 1976 to CA 1988.
One thing to keep in mind about LA is that it has been growing rapidly with the entire metro area being contained within the county at one point of time. By the 1960s the metro area had started spilling over into the neighboring counties but still most of the LA area suburbs were within the county. By the late 80's though, most of the high growth areas (usually corresponding to heavily GOP areas) were outside the county and even more and more of the county became inner city areas (which were former suburbs). The priorities of the residents changed (if the residents themselves didn't change) and they started voting Democratic. But was there much of a difference between how the LA metro voted between 1976 and 1988? Not really. Ford did "better" in LA county and Bush did "better" in OC and the IE. In reality most of the differences just had to do with where the affluent suburban areas were in 1976 vs 1988.
Now let's compare 1988 to 2000 or 2004. Bush won the LA metro in 1988, but did his son even get close? In 2004 I think the Republicans cut it down to a single digit margin for the Democrats out of the entire metro area, but 2004 represents a high water mark for Latino support for Republicans. And in 2008 Obama won the metro with an enormous margin. It is this trend of the entire metro that should worry Republicans, not the fact that they don't do so well in LA neighborhoods that have thoroughly changed since the 1970s.