Thanks for your question.
The TRX is a great way to give support to the squat for those that need help as they work toward perfect form. If you are already there move to the single leg squat progression using the TRX only for balance as you need it. If you already can do a free single leg squat then you will not need the TRX to perform this exercise.
As for the lunge the TRX provides good value for almost all user levels with the balance lunge progression. You will likely have no problems with the normal balance lunge so progress to the crossing balance lunge to integrate a stronger glute reaction or abduct the free leg to functionally isolate the quadriceps. This can be made even more difficult by performing the movement with your arms orverhead which drives trunk extension and isolates the quadriceps even further as the glutes are unable to load.
You will also find as a higher level user that the suspended lunge series will give you some great training. As you master the movement add a plyometric hop out of the bottom, use rotations, heavy ball lifts and throws etc. This is a tremendous series of movements to build the single leg strength, balance and power that will transfer into life and athletics perfectly.
I hope that this helps to answer your questions.
Good luck