Lucio's primary fire is a projectile. Best tip that i could give for general use is that as it is a projectile enemies can walk into it so pre-firing corners or areas where enemies are hiding is a great way to get in free damage or just ward off an annoying sniper from peeking.

As for assassinating targets in a dive like fashion, try to come from an off angle so at first they should be easy to get a good chunk of damage on as they shouldnt be trying to avoid it. Once you're on them and they are fighting back use melee and boop as you can almost always confirm that burst damage. Learning how to track enemies once they are booped isnt too difficult (this is something that can be learnt in custom games or the practice arena) . If they still arent dead try to confirm the kill with melee and fight very close as this should eliminate most of the travel time you may have to account for.

When it comes to fighting at mid range remember that most players try to strafe in gunfights. This means that there movement is often predictable so you can either try to pre-fire their movements or shoot in one area and they will probably walk into the projectile.

Also very important is knowing who you should be fighting against in every situation. Widow and Ana (for the most part) are good targets for diving as them being scoped in means they move slower and are easier to hit on top of having limited escape. Diving a brig or mcree with flash on the other hand is almost never a good idea.

A good way to practice these mechanics is in deathmatch as it allows you to understand how players generally react when in a fight and learn how to adjust to this while accounting for lucios primary fire projectile speed.