Those are very nice pictures of a really lovely animal. My understanding is that tarantulas from the U.S. are pretty much harmless to human beings. Some tropical species may not be so harmless. Of course, all spiders bite, and are venomous to some extent. When Mark Twain was a gold miner in Nevada, most of his fellow miners kept them as pets in jars. Perhaps this is because, except for one very old lady who ran the house they all lived in, there were no women for companionship. Tarantulas beat nothing---I guess.

Down and dirty and cheap.
Remote cable release and a tripod.
Set the camera to manual exposure: bulb and 1/2 open aperture. Point the camera where the flashes are happening at that time. Focus on the clouds. Press and hold the release for about 30 second or until you capture or almost capture a strike. Release trigger after strike has concluded as you may capture multiple hits, reframe and try again. Occasionally "chimp" the monitor to check focus and exposure. Move around as the storm progresses. Adjust f-stop as ambient lighting gets darker. Experiment with ISO for the best results.

D70s and 18-35 af-d.

And o'yeah - Shoot in Raw.