Suitable choice for cross section of lightning arrester grounding electrode which may be a part of one grounding system is related to recommended grounding system resistance in this case. For related standard you can refer to IEEE 142 (2007) , in page 155,156 we can read:
"Lightning protection of power stations and substations includes the protection of station equipment by means of surge arresters (see Walsh). These arresters should be mounted on, or closely connected to, the frames of the principal equipment that they are protecting, especially transformers. They may also be mounted on the steel framework of the station or substation where all components are closely interconnected by means of the grounding grid. For satisfactory lightning protection, substation grounding network resistance must not exceed 5 ohm; for large stations, lower values are desirable.
The surge-arrester grounding conductor should be connected into the common station ground bus. As with lightning down conductors, the grounding conductor for surge arresters must be as short and straight as possible. The NEC requires that it be not less than 16 mm2 (6 AWG) for circuits of 1 kV and over, but larger sizes may be desirable to resist possible mechanical damage, corrosion, etc."