Lined Potion Vials are made by scholars. They use Tetranoid Loam made as a byproduct of creating Tetranoid Reagant from the 2nd tier rares coral and silver. I highly doubt you will find any for sale. You need Scholar Refining Volume 11 I believe to make all the above items plus one rare material.
How it breaks down is you first make Tetranoid Reagant using the rare material. You then make Lined Poison Vials using the Loam byproduct. Making perfect vials will yield you 3 lined poison vials.
Hope that helps.