I regularly bike in heavy rain and thunder/lightning storms (actually, just yesterday I was biking through some torrential rain). The lightning doesn't bother me at all, but most of Toronto has very tall trees, houses, and poles everywhere . . . if you live in a flat desert or something maybe there's more chance of lightning strike? The wet is no big deal if you keep a couple things in mind:
1. As AlanStache has demonstrated, it's a very bad idea to go through water if you don't regularly cycle the route and know where all the potholes are. This is doubly true of deep water.
2. Expect the wind to be fierce. It will buffet you quite a bit, and can come and go unexpectedly . . . sometimes it feels like an invisible leprechaun running around your bike and shoving you.
3. Be bright. Turn on your tail light, wear light clothing, have reflective stuff on your bike. Rain and thunderstorms makes it more difficult to see you.
4. Related to #1 . . . know your route. Really shitty weather is not when you want to be exploring a new place. You want to be able to get into your left turn lanes well in advance, you want to know where all the sharp corners are, you want to avoid the dangerous super fast roadways, etc.
5. Steel grates, painted lines, and manhole covers are more slippery when wet, so be cautions around these things. Braking takes longer when your rims are wet . . . so take this into account when approaching a stop or descending a hill.