Leila, I am very curious as to why you would be asking such a question when it is quite evident to your colleagues or to anyone who has benefited from your expertise, that you could have very easily provided as thorough and as forthright an answer as those who have been kind enough to respond. Does your experience and/or research lead you to a differing opinion? Based on your impressive resume and the expansive nature of your work, perhaps you could help shed some additional light on this topic.
You never want to pre-fatigue smaller muscles that need to be fresh for working larger muscles. It just creates a “weak link in the chain” from the beginning. But if you’re doing squats & lunges, you’re killing two birds with one stone – besides being great leg exercises, they’re two of the best core exercises I know. You can’t do either exercise in good form without your core muscles firing on all cylinders – it’s not happening.
Intentionally fatiguing the stabilizer muscles prior to performing any exercise will increase the possibility of injury. In the case of a squat or lunge, especially when loaded, the low back will be placed at a greater risk of injury. As the stabilizers are not actually the target muscles of the squat, fatiguing them prior to the exercise provides no added benefit, but does increase the risk of injury which is exactly what you do not want to do.