Using a relay like that is an interesting option, since it keeps the two sides more widely separated. However, it doesn't ground the antenna side (or in your case the sprinkler side) at all. I'm not enough of an expert on lightning to know for sure whether leaving it ungrounded is better or worse. If it arcs, it should arc to the grounded contact of the relay, but I would think that providing a solid ground connection in the first place would be better.
With antennas, you should always ground the coax shield, but I have seen differing opinions about what to do with the center conductor. The energy of the lightning strike needs to go somewhere, and if you don't provide a path, it will find a way of its own. Some people recommend grounding the center conductor of an antenna coax, others say just route the wire back outside the house and leave the center conductor connected to nothing. Leaving it connected to nothing doesn't seem like a good solution to me.
With antennas, you should always ground the coax shield, but I have seen differing opinions about what to do with the center conductor. The energy of the lightning strike needs to go somewhere, and if you don't provide a path, it will find a way of its own. Some people recommend grounding the center conductor of an antenna coax, others say just route the wire back outside the house and leave the center conductor connected to nothing. Leaving it connected to nothing doesn't seem like a good solution to me.