From what I know of, at least baby striders burn in lava. I don't know if adults do, I didn't try.

I found this when I was messing around with them dying in rain and I wondered if the got hurt when submerged in lava (They don't)

I then wondered if they did when in a lava cauldron, so I tested this and the burned, 

and I was very surprised, so I went to the nether and tried it there, and it still happened.

Thanks for listening 

-Enoki5708