I wonder whether a lightning conductor may actually attract lightning to the observatory area and cause more problems than it solves?
I have found some methods in Wikipedia to estimate the amount of required lightning protection and its effectiveness. Unfortunately only in German, as there seems to be no equivalent English entry. At least the Google-translation is mostly understandable, although Google's English is partly terrible.
Here is the German Link: http://de.wikipedia....iki/Blitzschutz
If you look at the chapter called "Rolling sphere method", you can see that even for the weakest lightning protection class IV, the maximum distance for which a lightning catcher can give protection from direct lightning is 60m, but only if your dome is 0cm high (unrealistic) and if the catcher is at least 60m high. For your 3.7m high dome, I would do the following math:
Sphere with r=60m touching a vertical catcher at x=0 and the floor y=0 (dimensions in meters):
(x-60)^2 + (y-60)^2 = 60^2; (Pythagoras)
=> x= 60 - sqrt(60^2 - (y-60)^2); (the other solution with opposite sign of the sqrt() makes no sense).
For your dome, y=3.7m. This results in x=39.256m. Anything farther away than this will not protect your dome according to the weakest lightning protection class IV. And even if there's something in exactly this distance, it must be at least 60m high. Needless to say that the trees in 50m distance, your house in 100m distance and the church in 400m distance offer no protection of class IV.
A similar calculation shows that a catcher on your dome (or the dome itself) will attract lightning from a radius of ca. 21m, if class IV is assumed and everything around your dome is flat (which is not the case: fence, mast).
I think the church (400m away) has a lightning conductor but I don't think any other buildings in the village have
I don't know the law in France, but in Germany the law says you need lightning protection if a lightning strike could either easily happen or have severe consequences (http://de.wikipedia....und_Blitzschutz). I think if a house burns down, that could be considered as a severe consequence. Anyhow, I am not aware of any modern house in Germany that doesn't have lightning protection.
Adding one [lightning conductor] to the dome may be difficult (how do I ground it with the dome rotating)?
There is a heavy steel ring that supports the dome. Maybe I could use this as a lightning conductor
As I am no expert for lightning, I would recommend to check the following with your electrician. Besides, I don't know the details of your dome.
Depending how the rotating dome is supported: if the bearing is massive and entirely electrically conducting (e.g. steel), I could imagine that a lightning conductor on the dome could be connected to the rotating part of the bearing, and that the fixed part of the bearing could be connected to the earthing system. If I had equipment for some 10000 EUR inside the dome, I would attach a grid of lightning conductors instead of a single one on the outside of the dome in the hope that they serve as a Faraday cage and reduce the field strength inside the dome in case of a direct or nearby lightning strike.
How to build the earthing system: there are several links in the article, but I think you should discuss it with your electrician. Reading the article, I have come to the conclusion that the Earth connector of the mains supply on its own is not sufficient. However, I still think it could make sense to connect the mains Earth to your Earthing device in an attempt to reduce the voltage differences between floor and mains in case of lightning.
I can't tell you if a conducting stake in the soil is sufficient. I assume it depends on its size and depth. Wikipedia says such devices ("Ground rods") may well be driven 9m or more into the soil ("nine feet" is a translation error by Google).
There are copper data cables to the main building from the observatory (two Cat6 shielded cables) but these also go underground.
Even if they are underground, I would think about adding a lightning arrestor where these cables enter you dome or your metal cages (if that exists for Ethernet), or at least ground the shield well. The electrostatic field of lightning can extend several meters below the Earth surface, because soil is not a perfect conductor.
Or you may consider an optical fiber cable instead of CAT6, because it is non-conducting and doesn't conduct lightning to your electronics. Besides, as far as I know, transmitting high data rates (>1Gbps) over large distances (100m?) is easier when fiber is used instead of copper.