You can only possess one LORE item at a time. *IF it's in the shared bank space at the bottom*, you can't pick up another on any alt, because it's in the account-wide domain. You can have as many LORE-EQUIP items as you want in bags or bank space, but can only put on 1.
The LORE tag on shinies is slightly different from the LORE tag on equipment and items. It allows for multiple shinies in a shared bank.