L1 is not declared in this scope error
I have the feeling you need only one state which can have 4 values: L1, L2, R1 or R2.

For this, use an enum:

enum EState { L1, L2, R1, R2 };


Now create one state variable of that type and give it an initial value.

EState state = L1;


Some other problems I see at first sight:

case L1:
  if (state == L1){
  if (button1State == HIGH){
      state == L2;
  }
}
break;


In this statement, when there is case L1, it means the code following ( until the break) is only handled when the state (because of switch(state) is L1, so you can remove the check if (state == L1). What is left is:

case L1:
  if (button1State == HIGH)
  {
    state == L2;
  }
  break;


Than you use state == L2 to set a new state. However, the == only compares two values, if you want to assign it, you have to use a single =, thus the code should be:

case L1:
  if (button1State == HIGH)
  {
    state = L2;
  }
  break;


Of course you have to do this also for the other case statements.

Tip: align your code (make the { and } aligned under each other; this will make your code readability much better.