With this lamp, you can summon a tressym when you cast the find familiar spell. If you become unattuned to the lamp, you lose any tressym you have summoned.
An oil lamp once possessed by an ancient elf mage who was obsessed with cats. One of her cats devoured her after she died and became a bakeneko (Japanese ghost cat). The PCs got this item after defeating the bakeneko. The lamp ties into the Japanese ghost story of the bakeneko, which is said to lick the oil out of lamps.
Tressyms are notoriously hard for wizards to summon, which is why they can't normally summon one as a familiar. The oil in the lamp draws the tressym to the summoner and makes it so they can reliably summon the tressym.