{From the mun: And the second ask. No, really, if anyone has any theories as to why the web version of my inbox hates this particular user, I would love to hear them. D: Again, so sorry!}

The first step is to earn his trust. This … is a bit of a complicated step. And it’s complicated because my advice on achieving it may seem a bit backwards to you, but in order to do it, train alongside your lucario. That means adopting many of its same behaviors, most notably its drive to train and its dedication to an honorable lifestyle. The more it respects you as a master, the more likely it will listen to you when you wish to engage in more relaxed activities.
If you’ve already achieved this point or once you’ve reached it, you may proceed by easing your lucario into the relationship you wish to have with him. Except with other members of their species, lucario are generally extremely serious and dedicated pokémon, so it’s highly unlikely you’ll ever have a fully relaxed one. However, you can coax yours to have fun now and then by introducing them to fun little by little. Give your lucario treats every so often. Turn some of your training routines into games. Progress slowly, adding more and more fun gradually until it literally becomes part of his daily life.
As you do this, always train alongside your lucario. Never force him to lead if he doesn’t want to. It’s all right if he simply wishes to follow you. But by engaging in the exact same training exercises as him, you will establish that you’re willing to put yourself on his level, rather than force him to rise to yours (in his eyes). That way, as time moves on, he’ll be more and more willing to accept that you are, in a sense, equal to him, which will allow him to relax a little more than usual around you.
Ultimately, however, keep in mind that some behaviors are simply inherent and that it’s sometimes counterproductive to force a pokémon to act in ways that are contradictory to who they are. But by reversing the thought process and putting yourself on their level by accepting them and reaching out to them, they may be able to accept you and feel more comfortable changing and adapting according to the steps you take to be their friend.