Lionsgate made huge profits from The Hunger Games and Twilight movie franchises so it's natural that the studio wants to keep making movies set in their unvierses. With all the Twilight and Hunger Games novels already adapted into films, they can either reboot the franchises or make new films featuring fresh stories that are not based on books just like what Warner Bros. and J.K. Rowling did with Fantastic Beasts and Where to Find Them.
Now, Lionsgate CEO Jon Feltheimer expressed the studio's interests to make more Hunger Games and Twilight films. Speaking to Variety, he said that the studio will only move forward with "fresh installments or spin-offs" in the franchises if authors Suzanne Collins (The Hunger Games) and Stephenie Meyer (Twilight) approves them.
As of right now, both authors haven't released any new books within their respective franchises so Lionsgate have nothing to adapt. They will have to come up with new stories set in those universes. Perhaps the authors could collaborate on writing the script as J.K. Rowling did with the Harry Potter spin-off. Lionsgate is aware that these movie franchises each have a solid fanbase but to squeeze the tits out of cows with no milk left is just not the way to do it.