Lightning would be the least of your concerns with that type of mount. Tree growth would be a bigger issue. As the tree grows, it will cause your dish to go out of alignment...not to mention the increased chance of a branch falling on it.
Unless the tree is very dead, free of bark and with a suitable flat for the mating surface, I'd say no. Vital trees tend to do more than a little shifting around based on season; not to mention that they continue to grow pretty much until they die.
I've had my dish mounted to the trunk of a 12" tree for 5 years. We live deep in the woods, and this smallish tree was well protected from the wind until just recently. Last weekend the wind was moving the tree around enough to cause dropouts. I'm looking at moving to a pole mount.
I'm not sure I'll be able to get the mount off the tree. The bark has grown around and over the mount!
Just a bit of different perspective on this query. About 10 years ago, my uncle leased a cattle farm with a small farmhouse. I lived there rent-free for taking care of the cows. Great deal for an 18 year old. Anyways, got D*, and the tech came out and mounted the dish to a big tree close to the house. I didn't think anything of it and it worked, so that's all I cared about. Well, about 3 months later, I woke up with no D* service. After I realized there was 0 signal getting to the box, I went out and found the arm of the dish broken off and hanging from the cable. Turned out, the cows came up and scratched their heads and necks against the satellite dish and one of them ended up breaking it. So, I can't speak for tree growth or wind, but cows can definitely mess up a tree mounted dish!
This is my least favorite way of mounting any dish but here in the mountains of east Tenn. it's some what common in the steep terrain areas.
If you do mount a dish to a tree you will likely need a realignments every 2-3 years "major shifts can occur in one season" and overhanging branches may become a big issue as well.
I would rather cut a tree and do a pole mount than mount one to a tree.