Think of it more like a Pika/Fox. It's not attacking while in the process of retreating that's a big deal (Link style), it's how anytime he's near or far from you, you can get instantly approached by something that could lead to your death, so you have to chase him. Just like fighting Fox/Pika, they can just go wherever they want without a big deal, and you gotta deal with whatever they do/make them fight for it
Eh, I honestly see that as more of a generalization of what I was discussing rather than something different. I'm not talking about hopping back and throwing stuff out to cover your ass Link-style, I'm talking about dashing back when your opponent enters an awkward spacing zone, and stopping precisely where and when you want to punish, usually through jumping/pivots/turnarounds (this is basically a "retreat" as the term would be used in, say, fencing, rather than military tactics, sorry for my confusing terminology).
Every maneuver in the DD game, dashing or not, works towards setting up a distinct action that ends neutral. This DD/neutral endgame is theoretically where commitments should be happening, so if Lucas isn't committing, yet transitions into punishes, the precise reversals out of neutral movement that make this possible may deserve to be understood more instead of being glossed over, so the actual root of the issue can be discussed.
In fact, Lucas' exceptionally powerful options (e.g. DJC, which essentially offers him an expanded pseudo-pivot game, or the zair/grab combined coverage I mentioned earlier) all tend to apply as something you want to decisively end neutral with rather than delay until things happen; he just doesn't have the speed or hitbox coverage to disengage indefinitely without being cornered.
DD game isn't just dash speed. DJC instant Fair without losing position/movement/committing at all, is just as much of the DD game as anything. Just like SH Nairs from Pika/Fox is.
I implied that it wasn't just dash speed, myself, which is why I brought up pivots, DJC, RAR, etc. It still means that, when compared to other, faster characters, Lucas is starting with a measurable disadvantage, because he can't hang back as far, and takes longer to space, leaving less time to punish. I sort of view it as Lucas gaining less leverage in spacing for each micro-action he takes, thus setting up his desired endgame less rapidly and with more effort.
Also, I think that you might be exaggerating DJC fair's control a little bit. It's only 0 at best on shield, and maintaining safety requires that you follow up with magnet or back off (i.e. lose positioning), assuming your opponent lacks frame 5 OoS or faster. If it allows WD back or even a jump from your opponent to become difficult options to chase, wouldn't that be a loss of movement, too?