As I understand it Advanced ones are needed on bind on pickup, such as items from Boss drops in instances, quest reward items, and shell gear from vendors. What happens after using a lifter on these? Does it remove the bound mechanic completely, or does it make it a bind on equip? If it makes it bind on equip, can a normal lifter be used on it from that point on?
Yes, the understanding is correct. After removing BOP condition, item becomes BOE and needs regular lifter.
It is also the case that regular BL will not get used up if it does not work. So, if you have item and you are not sure if it needs BL or ABL, try BL first.