I had a Sigma IV in a very tall tree for many years. Since it was DC grounded and had 9913 coax on it, I just grounded the braid to a 8 foot ground rod right at the base of the tree. I added a few radials to the ground rod with a garden edger to help disperse any lightning currents. Approximately 60 feet of coax was also buried with the garden edger to make the run from the tree to the house.
During one storm the antenna took a direct hit by lightning while the radio was on. I was in the room near windows to see what happened and the flash of light from the tree top was as blinding as the thunder was deafening. The radio that was connected to it was a mobile, powered from a Motorola 20 amp two-way base power supply and everything went off after the strike.
When the storm passed I was amazed that the only thing that seemed to be damaged was the primary fuse on the 12 volt power supply. I put a new fuse in and everything powered up working good! I was expecting shorted pass transistors in the power supply, blown final in the radio, burnt up front and RF transformers but none of this happened. Most of the energy was dissipated at the ground rod and what remained was capacitively coupled to ground by the buried coax.
Years later I moved from this location and left the antenna in the top of the 80 foot oak tree still grounded. I received a phone call from the new residents who informed me the antenna had been struck again! The second strike burnt the top right off the Sigma and I found parts it in the yard when I went up to look. The coax was still rolled up in the house and the connector appeared intact with no arcs. I cut that and removed it from entering the house.
If you place a antenna in a tall tree where it could be struck by lightning, try to burry at least 25 feet of coax from the base of the tree before entering the house. Rather then cut the coax at the base of the tree to attach the ground to the braid, consider just removing a portion of the outer jacket to make this connection and then seal it up. That way you will not create any impedance bump in the transmission line.
Note: The Sigma IV has perhaps one of the best DC grounded designs of any antenna. The entire heavy gauge aluminum radiator is directly connected to the RF grounded base, not through a matching network, inductor or shunt coil. The gamma match also creates DC isolation on the center conductor of the coax. If the base of the antenna or coax braid is properly grounded, these characteristics make it much more likely equipment can survive a lighting strike. Not all antennas will perform this way.