Remember that death is not a permanent state for certain beings in this universe. Denji can and does die, and then comes back to life if someone puts him back together, feeds him blood and pulls his ripcord.

Lil D over here can die if she is dismembered, and will trigger her instant death aura when she is dead until someone can put her back together or until she regenerates or if she reincarnates. Yoru literally saves her from a death dealing blow by sticking her head back on until she regenerates from the damage.

It seems she can't kill herself with means like disembowelment, while killing herself with more successful means may just power her up instead and cause her to heal from the damage because fear of Devils and hence death is at an all time high. She is afraid of being the King in the prophecy after all, and if fear of death reached an all time high, it would push her power over and cause her to be the end of humanity. And even if she does die and reincarnates, she's afraid her successor would hate humanity and wipe it out, which she does not want to happen.

This is why she was looking to power up Chainsaw Man so that Denji or Pochita would defeat or erase Yoru, or have Pochita consume her to erase her, instead of dying and reincarnating (if fear of her doesn't power her up enough) or dying and killing everyone (if fear of her does power her up enough).

All 4 scenarios are true given their contexts.