It may seem like it doesn't matter at first, but think about it.

For an Imperial this is about more than allegiances and politics.

For the natives of Cyrodiil, the Empire is the embodiment of their very culture and history.

Would it be right to deny Lucia her heritage?

I know, your character is supposed to be more than labels, but his/her opinion of her people's culture is inevitably negative.

Probably not the best person to guide Lucia towards getting in touch with it.

If Lucia does not know she is an imperial does it matter for her if she is an imperial or Stormcloak?

Is it not enough for Lucia being the daughter of the Dragonborn?

She's an orphan who was most likely born in Skyrim and apparently still has relatives living in there. I don't think she'll care about whether she's brought up as a Cyrod or a Nord or whatever so long as she has a home and a family. (That isn't her awful aunt/uncle)

If she cares about her heritage she'll probably seek it out herself when she's older.

For now.

But she will grow up.

The whole point of the stormcloak rebellion is because the empire has failed and now a puppet of the thamlor (and maybe ulfric wanting to be high king ) I would teach Lucia her imperial Heritage but I would also teach her how and why the empire has failed and why the stormcloaks are rebelling against it.

or you could adopt Lucia in windhelm, not only is she an stormcloak kid but living in windhelm as an orphan must be a lot harder than whiterun

She will grow up with the values her adoptive parents instill on her. Personally I would teach her about her heritage if she seems interested in it, but won't force it if she has no interest in it.

Also this!

They all do, or they don't. Maybe she will start asking questions, maybe not.

I think that is something you will have to handle when that time comes.

Or... you could turn her into a vampire and she will stay at the same age forever. Eventually she will find out, but maybe she won't.

She's a child, what she needs right now is a home and a loving family, not a lesson in Imperial history. You're worried she'll be out of touch with her people, but this is going to be the least of her problems if she grows up as a beggar on the streets. Just take her in, give her a new home and let her decide for herself when she gets older.

I don’t see an issue unless you make one. Lucia does not complain when you approach her wearing Stormcloak armor. It’s up to the player and how she works in your story. You could have a staunch Stormcloak see Lucia as only her race and make assumptions about her culture. You could also have your character treat the child as an individual and raise her with an open mind. Your choice.