Page 63 is just like the foresight on page 2, except for the tree. The Dad guy never saw this coming in any future "branch".
On a tree, all potential branches that could be stem from a trunk that was and is. If Dad's power is to see all branches that might arise from the current trunk (Lucas in this case), then, for an unforeseen branch to occur, it must stem from an alternate trunk, an alternate timeline, or perhaps even be "rooted" in the Future-itself, not as what must logically follow the present (in turn becoming present then past), but as the formless object of pure hype (which remains ever future), the essence of "dreams".
Considering the context and themes, my guess is the latter. In any case, this brings up the question of how could he possibly tap into whatever he tapped into.
At some point, it was mentioned that a ramus flowering was triggered by feelings of affection, and it's clear that Zoe matters a lot to Lucas. In his "vision" (which is panneled suspiciously like Dad's foresights), he has escaped from the wars with Zoe and is living happily, presumably as a musician, but they are caught up by the Garland's onslaught. There simply never was a path for his dream in this world: the "flower" of his life doesn't even potentially exist, not even as a footnote on the world's DNA.
The full realization of this fact must have pushed him beyond regret, beyond the deepest despair: knowing that the world had strictly no space for his dream must have freed his dream from the world's logic, from any sense of expectation, debt, or responsibility towards it. Something akin to how behelits are activated in Berserk.
This, I believe, is how he, or rather his desire, broke through the world's Logos, if perhaps only for an instant. His power is essentially the power to communicate one's desire without words. Taken in another way, his power is the proper language of Desire, a language which is not other than Desire (for only Desire can expound Desire), but rather the manifestation of a hitherto unknown aspect of Desire.
Even as action, speech, and thought move along various desires, so do move along Lucas' "constellations" those to whom he shows them. Although it has only been used as a way to extend his motor will beyond his limbs, it might well be used to communicate much deeper desires, perhaps including desires which are not even footnotes on the world's DNA.
We can see on page 60 that he was led to his vision by one of his "constellations". Among other things, this means that this power is unrelated to playing the bugle. Keeping in mind all the above, it follows that the only reason why he needs to play it to manifest them is because music is the "foothold" of his dream, the one "part" of it which overlaps with the world, the one part of the world that is "conductive" to the Desire-energy in him.
If his dream found new footholds (or if the current one was expounded and thus "expanded" it to seemingly different things), his power would evolve as well. Most importantly, how would his power synergize with Zoe's ? Zoe who can weave Time, guided by Lucas who can exactly communicate one's desires, and whose dream reaches outside the world's timeline, thereby overcoming Zoe's limitation... What kind of Future might this pair bring to Existence ?
I mentioned One Piece kinda randomly last chapter, but this synergy would strongly parallel one that was implied in chapter 1103 and shown in chapter 1118.
Not unrelated is the matter of "saplings". If flowering is triggered by affection, then the full growth should not be much different. At least, it must certainly be fueled by intense feelings. Perhaps there are only a select few who can feel such feelings. In any case, since these saplings are the core of the towers, and the social order depends on these towers, we can say that the world's order is founded upon the sacrifice of the deepest human desires.
My guess is that such desires, intense as they are, are still bound to the world's logic, and Lucas' no longer is. Since towers are themselves grown rami, might Lucas not become something like a rogue tower at some point ? That would allow him to live freely, as well as other rami who would live around him, as he could power them too.