I'd been watching a Let's Play of Skyrim on YouTube, and while the person was in Whiterun, he came across a little girl called Lucia. In all the times I've played Skyrim, I've never seen her at all. I looked on the wiki and it said that she may be stuck in Carlotta Valentia's house, but she wasn't there either.

Is there any way to fix this?

Lucia is an orphan you can adopt. By day she sits or hangs around the gildergreen tree in the center of Whiterun. In the evening you can find her inside the Bannered Mare.

You need Hearthfire DLC for her to appear in your game.

Like Res said, Buy the hearthfire DLC and she'll be added.

The DLC is pretty good if you like RP-ing.

If it's nighttime, she'll be either in the Bannered Mare, or sleeping in an alley behind it. It's enough to break your heart. Especially when she asks you to be her mother/father.

There's a similar girl selling flowers in Windhelm. Wait at the door to the docks to find her. But again, Hearthfire must be purchased and installed for her to show up.