What is the best exercise for the lower abs and the side abs?
I am sorry to let you down here but there no such best exercise for lower abs or the side abs. i would like to tell you that side abs are in fact called as obliques.
However there are exercises which are very effective for the lower abs and obliques meaning they work better on these muscles in comparison to your other abdominal muscles.
For your lower abs reverse crunches, lying or hanging leg raises are great exercises to incorporate. Once your core gets stronger you can even use weights like a dumbell to perform these exercises.
For the obliques great exercises to perform are woodcutter chops, Russian twists.