What we know about lightning. An electrical charge develops in sky (mostly in storm clouds), as the charged area moves with the cloud an opposite charge intensifies in the ground underneath. These electrical charges send out 'feelers' as they try to get together, as these feelers ionize the air the conductivity of the air is reduced and finally the two charges come together and pass a huge amount of electrical energy. The huge current flow induces (electromagnetic field) voltage and current in nearby wiring, a voltage spike that will burn outlets and jap anything that is connected.
My take on this; grounded objects (with relatively low resistance to ground) are the ones that usually get hit.... trees, houses, tall buildings, etc. That's why you're safer in a car (rubber tires), wearing rubber boots, etc.
Grounding the antenna is a catch 22, if grounded the electrical charge can intensify more than the house roof itself due to the low resistance path to ground (increase your odds of getting hit?), but you couldn't buy a ground wire big enough to pass the thousands of amps a lightning bolt can have without vaporizing somewhere so there will be damages. If ungrounded the coax shield connection between the antenna and your electronic device (TV) provides a path to ground at the electronic device. A surge protector may help prevent damage from the voltage spikes in the electrical wiring, but this doesn't help with the coax itself.
My opinion, leave it ungrounded and disconnect electronic equipment from the coax and electrical power during a severe storm overhead or very close by, at least it will save the electronics. Nothing can really protect you from the possibility of getting a lightning hit, but the overall odds you will not be are in your favor.