The word ليس means, roughly speaking, "is not". It is a combination of لا and أيس (a word that is not used on its own but historically it means something like "being").
You often use ليس to translate negative sentences in present continuous ("I am not eating meat (right now)") and لا to translate present simple ("I do not eat meat (ever)"). But this is not exact science. As you can see "does not have" also translates with ليس. The sentence more literally means "there is no new scarf with Judy (in Judy's possession)". Hope it helps
As always please correct me if I'm wrong, I'm just learning.