Yes, the High Voltage discharge probably generates x-rays.
No, the x-rays are probably not dangerous as long as you are far enough away. If you are too close to the lightning strike x-rays are the least of your worries.
Radiation Field decreases as the square of distance (I realize this is a simplification I Want to be at least 1/2 the distance of the average length of the lightning bolt away so it will be a point source <inside 1/2length treat it as a line source Rad. decreases proportional to distance>)
Since I have no idea how much x-ray radiation a lightning strike puts out lets assume at 1 meter away you will get 40 REM (which is probably much too high), and the stroke is 1kM long: at 10M (Way too close for comfort) that's 4 REM at 100M (close)thats 400 millirem at 1kM (typical) thats 20mr, Note this is all before taking into account any shielding effects from air, rain, haze, and your brick house.
Note 2: point source = proportional surface arae of spheres
line source = proportional surface area of right
circular cylinder
If you want better data try placing a scintillation detector calibrated for X-rays (appropriate keV for lightning kV) near a lighning rod or other frequently struck object with a data recorder. I don't recommend using geiger counters or pocket dosimeters ( of the capacative discharge type, ie old civil defense models) since the ionized air will give all kinds of erroneous readings, a ThermoLuminescent Dosimeter <TLD> would probably be OK just compare it to a reference TLD. Of course this should all be set up prior to the thunderstorm, doing so while the lighning is striking could be dangerous, but if that's your kind of thing try it with a kite like Ben Franklin (If you do THAT dont blame me for what happens, that part about the kite WAS A JOKE)
Even if we are exposed to a little radiation from lighning every now and then remember we also get about 300mr a year or so from Natural sources even from our own bodies, so since people in Central Florida (Lightning Central, USA) don't seem to show radiation sickness. The dangers of Lightning generated x-rays seem negligible, in comparison to the lightning itself. After all how close does lightning strike, usually.
I hope someone can give some better figures than I did, because I'm tempted to try this experiment myself.
Best pure curiousity question In a long time.
-Dan76