No, the cable itself will not have any protection.
What you should do at a minimum is ground the mount for the antenna to a metal cold water pipe, or better yet, use a ground rod. By grounding the antenna base, you would also ground the outer shield of the coaxial cable.
Ideally you would want a supressor on the feed line. Something like a polyphaser device would help protect your equipment, but to be on the safe side, you should disconnect your scanner when not using it, or when storms kick up in your area.
LMR-400 and a discone would work well, however don't overlook some of the multi-band vertical antennas out there. Discones work well at covering a lot of frequenices, but don't necessarily do it well. They are sort of on one side of the compromise spectrum.
There are entire books written on grounding systems, way more than I could type here. There are a lot of fine details that go into the area of the National Electric Code. You really need to do some research here.
What I can tell you about antenna systems is that you get out of them what you put in. If you cut corners on your antenna system, your system will suffer as a whole.