Alright cannot remember where this came from exactly bit part of Lucy's inspirations include her face being based on a human counterpart of sorts. Lucy's face is uncannily similar to Greta Hoffman, same face structure down to the placement of the mole.
Now consider Engima's relationship to Lucy - its initally already tense as initaly he sees the Awakened a threat in a sense to the Humans in Laplace, maybe he viewed her appointment to head of Laplace after the reversal of the previous Head as the Foundation attempting to place human staff with effectively robots.
Her face would have been a recent addition (the replaceable one) - its too similar to Greta to be a concidence, after all we know Lucy had interacted with both Hoffmans if we read between the lines when Engima corrects her at the end when she calls him Hoffman and not Engima. Wonder what was the story there - why Greta of all people? Lucy as the awakened valued progress as seen in her anecdote following the creation of flight. Maybe she saw that idealism and progression in Greta Hoffman maybe? A role model? Its hard to discern.
Back to Engima, it probably haunts him to know Lucy essentially wears his dead sister's face around, initially its off putting but by the end of 1.9 maybe it becomes a strength: Lucy keeping that mask means no matter what Greta will always be remembered. Maybe him at the end resolving to continue Lucy's work and better himself is partially because Lucy maybe reminds him of Greta, not just in face but drive.
Summary: Engima and Lucy's dynamic is interesting, especially when you consider that uncanny nature of Lucy having a face similar to Greta
