The more reliable way to check your lower control arm is to jack the car up and pry the control arm. "Speed bump test" or hard braking or whatever else was mentioned does not isolate the control arm and the behavior of the car in response to these "tests" does not tell you anything definitive.

A good quality LCA installed correctly will not fail at the mileage described. I would definitely rule out the upper strut mounts before doing anything. In bad enough condition those can allow the strut to wander, which in turn allows the hub to move along with it. This ends up with very similar symptoms to a bad LCA. Remove the wheel and pry at the strut, it should not have any discernible play.