I presume you mean domesticated cats, as lions are mentioned quite frequently.
The bible was written from the perspective of the decedents of Abraham. For the earliest part of their history, they were a nomadic, herding, people. The word "Hebrew" means "wanderer". As anyone who has even known someone with a cat knows, herding cats is not terribly easy, if it's possible at all.
Unlike domesticated dogs, which will follow their "pack" instinct, and wander with the herders and work together for the greater good, cats are individualistic and territorial. These are better suited for farms and cities, where grain storage attracted prey for the cats, and the presence of cats were a benefit to the stationary dwellers (protecting their stores of grain) first tolerated, then encouraged, and finally embraced.
There is some evidence that cats were first domesticated in Egypt by the nobility. As the Egyptians were considered for the most part, evil masters, the Hebrews associated cats with their enslavement and never developed traditions about them.
Thus they are simply not mentioned.