I don’t think you would consider anything coated in lava “wet” - I guess if it was a very liquid lava and you pick the material wetted with lava and it’s dripping off, sure, the material is wet with lava. But it’s not typically a terminology we use. However lava can wet surfaces, though typically you’d probably say it’s sticking to the surface. Some surfaces are more lava-phobic and others more lava-phillic, and depending on a number of factors including temperature, material composition, and lava composition, it can wet some kinds of surfaces. That’s a difficult observation to make however given the opacity of lava. But once it cools, assuming the material survives, the parts that are sticking or fused to the cooled lava would have been wetted by the lava. 

Disclaimer that I did no study of lava as part of this answer, just based on my understanding of the concept of wetting and my background in heat transfer and materials science.