If L and S are pointing in opposite direction:
The value of J would become minimal, meaning the the energy will become minimal as well. If L and S are equal, J would be zero. This corresponds to a negative contribution to the energy, due to the value of S and L. This must correspond to the lowest energy state.
If L and S are parallel:
The sum of the two values of L and S must be taken as they have exactly the same orientation. This means the contribution to the energy is the highest. This must correspond to the highest energy state.
If L and S are perpendicular:
The J vector, would orient slightly to The vector which has the most upward or downward diretion. The total energy contribution will still be negative, but less than the extreme case, where the orientations are antiparallel.