I won't cover what _Alex_ just did, namely in terms of abilities, but I can provide some tips on the weapon itself.
One of the L-3 D's major strengths is turf coverage and, accompanying that, an ability to breed specials (though since it is more of a midline weapon, you probably will be splatted more regularly than the average special breeder). At the same time, however, its kit allows the L-3 D to hone its slaying tendencies and obtain the needed splats. Using Burst Bombs to finish off weakened opponents is immensely useful, especially if using aforementioned MPU. Another personal recommendation of mine is to practice with the Inkjet; you will be using it quite often with this weapon and it is a great tool to push forward.
In terms of priorities during battles, I would say that as a strong painting weapon and, simultaneously, an effective slayer (depending on your skill and practice), you could place equal preference on gaining map control and splatting enemies. The L-3 has a longer range than most people think, so you can surprise them with a few quick bursts. Accuracy is key with this weapon, as well.
I hope this helped you a bit!