No. Nothing is known for certain.

She apparently died in Syracuse in or around 304 CE, but the first written account of her life didn't show up until around a century later. It also contains a lot of literary devices common in martyrdom accounts, bringing into question how much of it can be considered accurate, and how much is simply an attempt to fill out the classic sacred virgin martyr romance narrative. Her story is remarkably similar, for example, to Saint Agatha, who is even directly mentioned in Lucia's hagiography. It's likely that parts of Lucia's narrative was written to meet early Christian literary expectations.

Jacobus de Voragine's Legenda Aurea (a much later work) describes her family as noble and wealthy. And her mother's name was Greek, Eutychia. So it's possible that she came from Syracuse's upper classes and likely was descended (at least in part) from the Syracusan Greek population. Speculatively that likely would mean she was olive skinned and had wavy to curly dark hair. Ultimately though we can't do much more than speculate.