It's very unlikely that front squats would work the lower traps to any significant degree.
The lower fibres of the trapezius are responsible for the following movements of the scapula1:
- Upper rotation (in which the lowest point of the shoulder blade moves laterally and upward)
- Adduction (in which the shoulder blades pull together)
- Depression (in which the shoulder blades move down)
The front squat involves the scapulae being held in a position of upward rotation, abduction, and elevation. (I.e. The shoulder blades move out around the sides of the rib cage, and the shoulders are raised.) Of these positions, muscular tension is required to hold the shoulders in elevation against the weight of the bar.
Therefore, the main muscles of the shoulder involved in this exercise will be those that perform shoulder elevation - i.e. the middle and upper fibres of the trapezius, and the levator scapulae. (In addition, of course, to the main target muscles of the exercise - the quads and thoracic spinal erectors.)
If you specifically need to strengthen the lower traps, then shoulder depression movements (such as the dip shrug) and shoulder adduction movements (such as the Kelso shrug) would be beneficial, along with bent over row like movements.
However, it's quite an unusual goal to want to specifically strengthen the lower traps. Why do you want to do this?