I would be extremely wary of modifying a spell to give a better result. Think about every change as a new spell that you are giving away for free. But somehow only spellcasters get those benefits to their PC's versatility and thus to their overall power level - never the less-magical PCs. That doesn't seem very fair.
While the Rule of Cool is a real thing, and important, it is even more important to be fair. Most of all, ask yourself this question:
Is it a freak occurrence that is certain not to happen again?
If so, then go for it. Otherwise, expect the PCs to later try to abuse the opened exploit as much as they can.
Now, when the target is not in water, where does the electricity all go? As the spell is cast directly on a target, all the electricity goes inside it. But where does the electricity go afterwards? If it were "real" electricity, it would flow through the target's body and then into the ground. But here it is "magical" electricity. It just doesn't get out at all: it has done its damage, end of story.
In water, trying to apply "common sense" to this magic spell could lead to all kinds of weird results. Why would the electricity remain in the target to fully zap it, when there is so much water around to dissipate it? After all, electricity likes to flow where there is least resistance, right? So "realistic" logic could even say that the damage is actually reduced!
Even if you could target the water itself, instead of only a creature, then the electricity would just spread out and mostly go to the bottom directly. You don't get "extra" electricity; it is the same amount. So at best, if it spreads in a 10-foot radius, you take the damage and spread it between multiple targets - you don't multiply the damage!
You can also flip the situation around to guess that the whole thing is actually way out of whack, as in this example:
Initial situation: PC casts it on a target in water, gets the DM to give extra results for the spell, all nice and smiles all around. So far so good.
Flipped situation: PC casts it on a flying target. DM would have to be fair and this time the spell should do next to nothing, right? After all, if the spell works "way better" because water is such a good conductor, then the spell should work "way worse" because air is such a good insulator, right? But suddenly, this time players whine about unfairness and how their spells should work as written. Or they shut up, but are clearly unhappy.
So, if it is that badly unfair in the flipped situation, then it is also that badly unbalanced in the initial situation, too.
Since there are "realistic" arguments both to make the spell stronger (water is a good conductor!) and also to make it weaker (which can also mean it dissipates the electricity away from the PC better!), I just wouldn't mess with the spell at all.
Previous editions had complex rules about how elemental spells interacted with different environments, and those are all gone from D&D 5e - which is a very strong indication that in general spells should not be "adjudicated on the fly on a whim". Just let the spells do what they do "because magic".
The alternative is constantly risking opening a big can of worms each and every time.
Suddenly, that little single-target spell can damage up to 12 Medium-size targets that are standing in water. You've just given that guy area damage. And getting at least some water on the ground is not all that hard to do, too.
You would not make the fighter's "+1 light-emitting sword" suddenly gain the power to blind every foe around the instant he lights it up "because at night our eyes become extra sensitive against light, right?". Same thing here: avoid giving free unwarranted power boosts to spellcasters.
Sure, the Rule of cool is cool and all that. But 99% of the time you would instead paint yourself into a corner where suddenly that spell works way too strongly, way too often.
Say the PC is swimming in a water tank and suddenly gets entirely surrounded by not 12, but 50+ Small-sized water goblins that each have nice claws and teeth? No problem, cast the 1-target spell that is now a "lightning-fireball" and fry them all (taking a bit of damage, sure, but hey, it's better than getting attacked 26 times every round).
In short, how I would suggest ruling on this spell, for various reasons:
Based on RAW: no, the spell does what it states, nothing else.
Based on general common sense to avoid breaking game balance: also no.
Based on avoiding lots of future headaches against arguing players who, in the long run, will definitely start trying to exploit that "nice trick" as much as they can: also no.
It's important that for every on-the-fly ruling you make, you really have to it jot down, because it will be used by the players later on, and they'll expect you to apply the rules consistently. So, based on minimizing in-game overhead and needing to memorize all those house rules and future such headaches: also no.
But based on Rule of Cool: yes. And it is really the only reason to do so; everything else points to a very strong "No"!
But if you go with "yes", you definitely do not need to go overboard here! The most I would do is give advantage to the attack, just as if the target was wearing armor.
If I made the lightning "spread out", then the damage should also be "spread out". Now this can have very interesting game repercussions later on: when the group meets that blue dragon and they are near a shallow lake, they can remember that electricity attacks spread out in water, and decide to all jump into the lake. Now, instead of completely frying one PC at a time, the damage will be spread out - so they will all be pretty damaged, sure, but will probably win the fight instead of getting killed off one by one.
Basically, any house ruling you make can be used to benefit the players, whether you are boosting the power of a spell (PCs start to try to use it everywhere), or nerfing it (PCs start using that as a defense). But overall, I find that attack boosts tend to break the game more than defense boosts.