Yes. Lighting strikes water. When the clouds build up lots of + charge,and the water builds up lots of - charge, a "channel" of ionized air will form that acts just like a skinny wire between the clouds and the water. The charge will flow through the channel from the water to the clouds forming a lighting bolt. This flow of charge is electrical current.
Does it fry fish? Only at the surface of the water in the region at the strike. This is because the current flowing in the lightning bolt comes from a large area of the surface of the ocean. All that current is squeezed into the bolt. The current density is high in the lighting bolt and at the strike region, but the current density is very low far from the strike region.This is like pinching off the end of a hose to make the stream of
water more intense. The current is flowing on the ocean, but is pinched into the lightning bolt near the strike. So the fish right at the lighting strike would probably be fried.
However, a fish that is not right at the surface will not get fried, since in the ocean the currents will only flow at the surface. This is because salt water is a conductor, and the currents from a lighting strike will only flow on the surface of a conductor. (By the way, this is why it is safe to be in a car in a lightning storm. The car is metal, so the currents will just flow on the surface of the car and not go inside).
So the answer is this: Only fish at the point of the lightning strike near the surface of the sea will get fried. But if the fish is at the floating at the surface it's probably already dead anyways so being hit by lightning is no big deal.

Well, I know that lightening can strike water because I've have seen it happen.
About six years ago I was at Huntington Lake in the Sierras near Fresno. I
was on the shore and the lightening strike hit about 500 yards away from the
shore. It was pretty exciting.

As far as whether fish can be hurt by such a lightening strike, I guess it
depends on whether any fish are unlucky enough to be near the strike. How
close to the strike do you think is too close? I'm sure the answer is similar to
the answer to "how close is too close on land?".

That's a neat question. I think the first thing you should do is to look up the word ground. Try to find what it means in the "electrical" sense of the word. When you find that definition, ask yourself what would happen to electricity that struck a body of water in contact with the earth. Good luck. If you need any more clues, let me know!

Lightning definitely strikes the ocean, many thousands of times a day. There are about 5 million lightning flashes per day in the world and even though 70% of the surface of the earth is covered by water, only10% of lightning hits the oceans.

On land lightning is one of the most dangerous and damaging natural disasters, and can cause fires and injuries. The temperature of a bolt is hotter than the surface of the sun, and lightning can travel at 72 million miles per hour.

The damage from the immense power of a lightning bolt is caused mainly by electricity flowing through an object (a tree or person or house). Since the entire ocean acts as a conductor, the flow of electricity is spread across a large volume, and the energy would tend to go around a fish, rather than through it. It is like being surrounded by lightning rods, which give the electricity a clear path to travel. Therefore, lightning probably doesn't fry many fish except for fairly near where the bolt strikes.

This doesn't meant that it is safer for you to be out on the ocean in a boat, or swimming in a pool when there is lightning -- because you stick up out of the water, you will actually be more likely to be hit.

Try the Lightning FAQ:
http://dpo.ori.u-tokyo.ac.jp/ocean/FAQ/DJA08E.I0L@emr1.emr.ca.html

Also, this page is pretty good.
http://www.jacksonville.net/~dldecker/Lightning.htm