Being that lava, when liquid, is clearly a liquid, that makes it technically wet. The rocks over which it flows are technically wet with lava. So yes, technically lava is wet, even though we wouldn't normally use the word “wet” in that way.
Also asked, when a fish is in water is it wet?
Yes, everything in the water is technically wet. But that is it's normal state and so does not have the same relevance as when we say that something in land is wet. A fish being wet is the status quo and has no immediate relevance.
Can a fish be wet?
It's not that fish are dry. But that our understanding of wet is based on not being in water, but being in air. When you get out of a pool, you are described as wet. Because humans created language, our language is based on being land animals who exist surrounded in air, not water.
Are all liquids wet?
Wet can be used to describe being dowsed in liquids such as beer, milk, juice, urine etc. All of these, however, are water-based. Can wet be used for a liquid that has no water? Can you be wet by mercury?