Due to the construction of the story (discussion with Zoraida) and the fact that Lucius is growing claws, I do not think this is the case.
Yep I think this is quite clear with the rat catcher guild interaction at the start of the story. I enjoyed the first part of this story.
The second part of the story is clumsier because it tries very hard to justify Lucius doing stuff he really has no place to do, especially wandering in the northern hills chasing puppets with a crew of lawyers.
The second "board meeting" where Perdita arrives and Yao is extremely rude to Marlow seems really out of place to me considering how the story was developping so far.
I think it would have been preferable to place Lucius in a story where he was doing something more subtle (covertly helping the Arcanists to undermine Marlow for example, or getting rid of a competitor on the board while making people think the culprit was an Arcanist or M&SU member), and leave Collodi's demise to somebody else.
On the other hand, Titania appeared to Lucius (in Ripples of Fate I think) and called him Captain (If my memory is accurate). Afterwards we have seen no sign of Lucius being affected by Titania's rise to power.
Additionally, this story does nothing to tie him to the Neverborn (he is a dual master...). We don't see anything of his cool new theme which is all about secret murders, false witnesses and mimics (on the NB side).
There were so many sub-stories that could have been picked for Lucius, I don't get why it had to be killing Collodi and why it was done without introducing any of his 2 new henchmen.