Here in Dallas at the Cedar Hill tower "farm" there are 11 plus towers over 1500 feet tall. They always take hits during storms. At most as Goat Rodeo Cowboy said, you will get a VSWR "overload" and that's about it whether the transmitter is tube or solid state. I've ran both. Continental combined tube type (816R series) and Nautel solid state (NV-40).
I do slightly disagree with Goat Rodeo Cowboy on the vulnerability of the FM and TV transmitter towers over AM transmitter towers since the AM feedline does run from the transmitter output though the phaser (if used) all the way out to the matching network at the tower...these days typically an unbalanced or coaxial type feedline. The coax/feedline is grounded at the network in the tuning house, with the "hot" side attached to the tower. With the tuning network grounded at the tower, the lightning "usually" stops there unless the ground is compromised...
From my experience FM/TV towers are in general less susceptible to strike damage since the transmission feedline is bonded every 50 feet or so, down the entire length of the tower. In times past when some of my sites used individual rather than master antenna systems, we would take a strike which would damage a bay. But that was a rare occasion since the mass of the support structure (the tower) usually attracted the strike.
On some FM/TV towers you will see lightning and corona discharge devices which resemble metallic whisk brooms mounted above the the top of the tower to direct the strike to the mass of the tower. AM towers, unless they are shunt fed, are mounted on a base insulator and rely on the "johnny balls" (spark gap) at the base to "arc over" to protect the tuning network, the phaser and transmitter. This spark gap is set so it is wide enough not to flash over on modulation peaks, when the RF P.E.P. is at maximum, and yet set close enough to provide the lightning strike a low resistive path to ground at the base of the tower..yet another reason for the multiple 4 inch copper ground straps from the base insulator to the ground radials...
There are no "Sure Bet" ways to protect from a hardcore lightning strike. If the strike can pass though 6 miles of AIR, there's not much in the way of a man made insulator that can stop one. At best you strive to create the least resistive path to ground, without having equipment in that path...
Usually when that path fails on an AM tower it's because of contamination (bird crap) on or mis-adjustment of the spark gap (gap to wide) which allows the lightning into the tuning house and points closer to the transmitter. In the early days of solid state AM when MOSFETS and power combiners were not as "robust" some stations would fire up the trusty GATES BC1xx and run it until the storm passed. Today's solid state AM transmitters DX-50, DX-10, etc are much more "forgiving"...