It was all about money. And hatred.
LVD hated that Charles Vallow "won", when he died, and she found out that the insurance policy funds went to Kay Woodcock. The only revenge? Kill JJ. Plus, LVD could continue to collect Social Security benefits for JJ.
Tylee, she would have never let LVD get rid of JJ, (kill) which is why she had to go first. And, she probably was bringing up issues about death of Charles Vallow.
At this point, it is not logic, or caring...Tylee and JJ were just barriers. Get rid of them, keep their money.
The fact that LVD could do this so easily, is really scary. Logically, none of this even makes sense. Just divorce Charles Vallow, leave Tylee and JJ, dump them. And go have a new relationship with CD.
In a way, LVD could be considered a "family annihilator". She eliminated her family to pursue another relationship. Not unlike Chris Watts. Whether she did it, or planned it, her family is dead, due to LVD.
Her case is interesting.