Can a second class passenger use the restroom on a cross country flight to LA?

As far as I'm aware, anybody can use the restrooms on a commercial aircraft. I can't imagine it any other way (are people supposed to just pee in a corner?).

Yes.

For sanitary reasons, restrooms are available to all passengers.

However, on airlines with First and or Business class, some restrooms are reserved only for those passengers

If you mean flying economy/coach...sure. But you are expected to use the restrooms that are in the economy/coach section of the airplane.

Typically, there will be one restroom at the front of the plane, which is supposed to be reserved for first class passengers and the pilot/first officer. In the back of the plane, there are 2-3 restrooms, which are for everyone else.

I say supposed to be reserved for 1st class because I see economy passengers "cross the curtain" all the time to use the restroom up front. And the flight attendants don't really seem to say anything. The only time they do say something is when a line starts to form near the cockpit or when a pilot is in the restroom.

If the aircraft is divided into classes (First, Business, Economy) then passengers are required to use the toilets in their section of the aircraft. That also means a First Class passenger is not supposed to go to the Economy section to use the toilet even though there may only be one or two toilets in First and the toilets in First are occupied.

No, restrooms are for first class only; other passengers have to use the toilet instead.