There is a related question on the Skeptics SE. The answers cite a number of press reports about injury to swimmers from lightning, though I don't think it's clear what exactly happened so I wouldn't read too much into it.
Fresh water isn't an especially good conductor of electricity. I don't have figures to hand but i would bet that human flesh is a better conductor of electricity than fresh water because it contains more dissolved electrolyte. So if you managed to build up a significant potential gradient in a body of water it would electrocute someone swimming in the water. How much current would flow, and whether it would be dangerous would be very hard to say. In the case of your wire in a lake I would guess you'd need to be very close to the wire for it to be significant. Specifically you'd need to be nearer the wire than the lake shore otherwise the current would simply flow to shore and then to ground.
So while it's possible, it doesn't seem likely to be an effective way of killing other contestants. I'd just stick pointy things in them instead as that appears to work well.
Response to comment:
I got curious about this, so I decided to do the experiment. Since I'm short of lakes, lightning and sacrificial victims my experiment is rather more modest:
My lake was a plastic bowl, the lightning was a 12V car charger and the electrocutee was a digital voltmeter. I started by measuring the voltage as a function of separation of my probes. The plastic box is 16cm long, so the last data point at 16cm separation is almost the whole length of the box. I did the experiment with fresh water and with 3.5% saline (same salt concentration as sea water).
You get what you'd expect i.e. a linear potential gradient. There's a big voltage drop at the electrode/water interface so the maximum poltential difference is only about 4V. It was also a bit variable when using saline as the electrodes started dissolving due to electrolysis (the scrifices I make for science) I wouldn't read too much into the difference. Saline and pure water are the same within experimental error.
Next I measured the current between the probes as a function of separation:
Be careful with this diagram as there's a factor of about 600 between the two sets of data. The saline gave currents from zero to 120 milliamps while fresh water gave currents of zero to 700 micro amps.
So have I proved you could electrocute someone in a lake with a potential diverted from lightning. Yes(ish). If you draw a circuit diagram representing the various paths current could flow it looks like:
The current has to flow from the wire to reach the victim and there will be a resistance $R_A$. Likewise the current leaving the victim has to flow to earth and there will be another resistance $R_B$. If these resistances are low, as in saline, a large current will flow, which is good for lightning based assasinations. The trouble is that the water around the victim acts as a resistor in parallel with the victim. A very low resistance means a large current, but the current will tend to flow around the victim not through them. Large resistances, as in pure water, will mean a low current but more of it will flow through the victim. In my experiment my ammeter has effectively zero resistance so the current always flows through it.
My guess is that there is an optimum resistivity that is low enough to keep the current fatally high, but but high enough not to divert the current around the victim. But I don't have the data to try and calculate what that might be. However my house in Chester is only a few miles from the sea, and we have been getting thunderstorms recently, so if there are any volunteers I feel another experiment coming on.