That complete guide you posted.
That's exactly what I meant about Peach being easily the most erratic character in the rooster. A skilled Peach will try to approach as safe as possible, and her combo potential is flexible and hard. (BTW, your neutral video is great, a excellent way to show her potential).
Now, as a Lucario player, obviously our projectiles are our "safest" tools and possibly our best option to rack up damage. But if we rely too much in the projectiles, we'll get punished by it soon. Our second best tool is our ranged attacks (yeah, bair and smashes have nice ranges), we have to use them wisely and occasional, because we'll get punished if we whiff.
Finally, our best option to this MU is to think out of the box IMO. Improvising, adapting, and moving will be key in this match-ups. This is definitely a dynamic MU. If you start abusing your momentum, or falling behind with the game speed, you'll lose a stock. I have to mention, that if we get stock in a combo, the best option for us is to cooperate and deal with it while trying to escape and maybe counter. If we try to challenge her combos or attacks, we'll have a bad time, racking up unnecessary damage and it might be too late to catch up.
To end this, I see this MU as a dance. Both players can have the lead, but we have to respect each other momentum or else bad things will happen.
It's the Royal Queen vs the Aura Guardian. Show some manners and respect the lady, but make her notice your aura potential and flashy fur.