Firstly, I'm pretty certain shooting a lightning bolt is physically impossible, making this completely magical. As such, you could technically have the result be whatever you wish, so long as you stay consistent.
Lightning is the result of a strong negative charge building in the air, attracting the positive charges in the ground to group together. Then, the negative charge bridges the gap (air) and collides with the positive charge (which actually comes up ever so slightly before impact). If you wish to shoot lightning at someone with physics involved, you basically have to have your wand, hand, etc. build a strong charge, and force the target to align the opposite charge. So if there's nothing majorly conductive near you, the lightning will want to go to the strongest opposite charge: your target.
Doing it that way makes it such that you aren't really shooting a lightning bolt, but rather manipulating charges such that a lightning bolt could potentially leap from you to hit them. The target would feel the "tingle" as their charges aligned, and could potentially use a "counterspell" to correct their alignment, if that's something your system could do. In that case, the lightning would sometimes still shoot, if another object could align its own charges in response (often the ground).
In terms of lightning hitting itself, my prediction would be that it simply wouldn't. However, that result does greatly depend on the charges. Objects impact each other based on the electrons of the material repelling each other. Thus, if the two lightning bolts had opposite charges, they'd be attracted to each other. So they impact, but then the charges would continue to arc through both people. So two lightning bolts would actually make it easier for the bolt to work/hit, but it'd hit them both. If the charges were the same, they'd repel. This could yield two different results.
If both people built a negative charge in their hands, and positive charges in their opponents body, the lightning would probably just go from their hands to hit themselves. On the off-chance that it goes for the opponent, the bolts would likely repel each other, but would simply bend around each other to hit the target anyway. It's also possible that, in building their charges, the lightning wouldn't have a strong enough pull to the target to be released in the first place.
If you want, you can use the Rule of Cool and just do what you want, having a Harry Potter type lightning. But if you wanted to counter actual lightning, you could do a couple things. Firstly, correct your charge alignment, as said earlier. Simple counterspell. Secondly, you could make alter you alignment to have the lightning flow through you most easily down a specified path, avoiding organs such as your heart. Think Avatar lightning redirection.
In the end, just keep in mind: electricity wants to take the path of least resistance. Air is pretty resistant, so having it travel through the air requires the source and the target to be so strongly attracted, with no easier path than a direct line to each other, that the air's resistance is overcome. It'd be easier to electrocute people by sending a shock to them through a conductive surface, like metal. If you want lightning to act realistically, you've gotta create a non-resistant path. Otherwise, use hand wavium and say it's magic.
Edit: As to the details of the magic system, it's basically "magical energy converted to effects" with no further explanation. Think Diablo game franchise, where blue mana is converted to fire, electricity and other sorts of physical and non-physical effects.
In the case of this, lightning may not work well. Is the mana/energy mimicking the effect, or becoming the effect? Mimicking is easier, because becoming the actual effect can be more complex. Fire requires fuel, lightning requires a path of least resistance, etc. If it's energy that's just mimicking an effect (fire = burn, lightning = shock), you can have it act in a simpler way, as though it's simple energy, such that opposing forces cancel.