Carlos, At a bare minimum, yes you have to have a ground rod at the base of the mast/tower per the National Electric Code, and bond it back to the main ground of the house. And bond your mast to the ground rod at the base if its metal. #6 is the minimum per the NEC. I always prefer #4 or #2 myself. You may not find the top of your ground rod at the main ground location. Depending on the age of your house you may (should) have a intersystem bond on the wire going down to that main ground rod. It might look like a small ground bar, with or without a plastic cover, or it may look like a fitting about 3inches long coming out of the bottom of you main disconnect with a piece of pvc going into it that has some green screws in it. This is where the phone company and cable company will add their ground wires to. You can bond you second ground to this. As long as you are bonded back to the main ground you can you can run a ground wire from the lighting arrestor over to the ground rod at the base of the mast. OH, and don't forget to run a braided ground from your equipment out to that ground rod at the mast too also to avoid a ground loop.
The details of the NEC actually tells you that you should install a grounding grid out from the base, with ground rods no closer than 8 feet separation and the bare copper & rods buried completely. Technically if you can't install a ground rod straight down you are allowed up to a 45 degree angle pointed away from the structure. Here in TN with as much rock as we have it is not uncommon for electricians to dig a deep trench and lay the ground rod in the bottom of the trench to be sure that all 8 ft are buried as required by the NEC.
Since my mast is attached to the end of my house I have a V shaped grid going out from the base, and the ground rod there, 90 deg apart the with rods at 8 & 16 ft out from the base of the mast with #2 hard drawn copper buried about 10 -12 inches down. (I chose the hard drawn since I have access to it, normal people would probably just use soft drawn) Yes mine is way over the requirements but I have a lot of lightning in my area so I wanted to be sure if I took a strike it would be directed away from the house. My vertical is higher than the power poles in the area so I'm overly cautious. In fact I just realized that my wire antennae for HF is pretty close to that height too.
One other thing to point out is that the "enclosure" you have installed, appears to be an AC disconnect, or similar, that has been gutted out. If you are running LMR400 you will find that it probably will not give you enough wire bending space to install the lighting arrestor. The lighting arrestor and connectors add up to be longer than you think. I did that using a 6x6x4 PVC J-Box and discovered it was too small. I still have wires hanging all over the place outside until I go get the box to clean up my install. I just haven't gone into town to pick up an 8x8 or 12x12 yet since I'm working from home. Be sure to check the minimum bend radius for the coax that you are using, and add up all of the items together to determine how much space that you need. Times Microwave specs for LMR400 says a minimum of 4 inch bend radius for flex applications, and one inch if it is a permanent stationary install, such as on the back of your rig. This is to avoid crushing the dielectric which could have adverse effects on your SWR and communications ability.
There is about a 10(?) page post / "argument" in the forums at QRZ about grounding if you are interested. It actually does have some good points that you can learn from. DISCLAIMER: In MY OPINION some of the points in that thread you may have to take with a grain of salt because there are some antagonists who have obviously never worked in the field, and are basing all of their arguments on theory, not on practical application, or even parts that are actually made. Remember its the internet and what may be OK in other countries may not be OK here.