Art by  Stickmanwww
He opened a couple of slots for quick sketches at cheap prices during a stream, and I thought, "Well, why not?"
So, here we have Thulssa Yii, with his pet iguana (which has no official name). For reference, that's an actual iguana, not one of his transformed victims.
As snakes are not a social species, Thulssa Yii has no capacity for empathy, so it's wrong to say he "loves" his pet iguana. It's more like he highly values the iguana because taking care of it serves as a hobby to occupy his highly focused intellect during his downtime (those moments between plots to take over the world). Like most people of extraordinary intellect, Thulssa Yii gets very tense if he has nothing to do, so keeping an actual pet provides him with a leisure activity to allow him to relax.

The reason why I picked an iguana is because Thulssa Yii is inspired by two sources. 1) the serpent-men of Valusia from the Conan mythos; and 2) Blofeld, from the Bond franchise. The iguana is supposed to be a parallel to Blofeld's cat and an iguana is a good choice for that, because anybody who's had both an iguana and a cat will tell you that the animal an iguana most resembles in behavior is a cat. They both have high independent streaks (due to not being truly domesticated), they are of similar intelligence, and both can bond to their owners if well taken care of, but otherwise don't actually care that much for people.
The iguana is very strongly bonded to Thulssa Yii because he is very serious about taking care of it and even though he does not share the same level of emotional attachment, he would be very distressed if something happened to it.