While most people know that if you aim ahead of a moving target you can land a hit, you can also aim in the opposite direction that they are 'dodging' if you see them trying to evade, typically in the same 'escape' direction but attack left when they are dodging right and by the time your attack hits they will have dodged left as well. You can also hit the same spot twice in quick succession and a dodgy target will end up killing themselves by disproving the theory of lightning striking twice.

Another option is just to pause and give yourself time. Most targets don't count how many shots you have, they just assume that you ran out if you pause long enough. This is especially useful when you level it up and have already fired the initial three shots.

Don't always use it to deal damage. If you have extra shots and have already shot once and can't find targets, then scout with them. Hit bushes or fire a line of shots up a lane. Hit some towers, or poke a sleeping dragon.

And if you haven't fired a shot, then just like holding your Q too long, let it run out, or cancel it with a move. Your cooldown will be shorter at least.

The range on this is ungodly.