I wrote that too. I mean I always got correctet in school when I said lilac instead of violet
Yes. The Danish word is from Italian, from Spanish, from Arabic, from Persian, from Sanskrit. The English is from the same ultimate origin but via the intermediary of French lilas (older spelling: lilac).
It's funny, because in my native language (Portuguese) we've got several words for the same colour: roxo (most common), violeta, lilás, púrpura (the latter two ones being related to the Danish lilla and the English purple) and lavanda (this one is more of a light purple), they all come from different languages so it's funny to see which language uses each root. :D