another thing you can't forget, is for as much as you train your lower back, IMO you need to train just as heavy for your abdominals to balance it all. If your routine is leaning more towards the PLing style you need to add in some weighted ab exercises.
Yes, training with compound movements train the core but i think that direct ab work is needed in order to balance the amount of work you put on your lower back. If you incorporate hypers or goodmorning, i think direct ab exercises with weight is needed in order to balance the front and back for the core.
If you look at west-side style programs, they all include direct ab work such as decline bench crunches with weight/cable crunches/roman chair leg raises w. db. For the amount of work you give your lower back you should give the same amount of work directly to your abdominal muscles and vice versa.
i know it sounded repetitive, but thats ok.