How did you manage to break a lower control arm?
The ball joint should have been replaced with the LCA.
In fact, I probably would've gone through and replaced most of the suspension on that side.
I doubt that the clicking noise is from the rack and pinion, possibly from the tie rod end though.
First thing is to carefully inspect the front subframe and unibody for anything that could be bent. If an LCA is broken there is a pretty good chance that there is some more damage to the car.
If all is good then I would replace all the bushings on the LCA, lower ball joint, tie rod end, and the CV axle.
I would also inspect the spring and strut very carefully to see if anything is bent or not in the correct position. Look on the upper metal shaft of the strut (inside the spring) for scoring.
The damage and possible cause of the sound may be very hard to trace and could take a lot of time to track down and fix.