HOW TO CLEAR LISBETH'S REQUEST AND UNLOCK THE ACCESSORIES ENHANCEMENT MACHINE
First of all we need to accept Lisbeth's Request in our expanded home, she'll ask for 5 Plated Mantle and 5 Plated Armor.
They're both dropped by Hakai Cyan and Hakai Crimson at the end of the Demon Cave, I suggest to kill the blue One first since when only 1 remain alive, it buffs himself like crazy, and the Blue one become too fast for my tastes.
Once you're done farming them talk back to lisbeth and she'll unlock the Accessories Enhancement Machine in your home.
For a detailed walkthrough check the video below: