ليس is a verb, it changes depending on the subject. For example:
هو ليس طبيب
هي ليست طبيبة
هم ليسوا أطباء
But لا doesn't change.
When you use ليس the meaning of the sentence becomes like this: A is not B (you cam apply this on Aasem's sentences)
لا is used with other verbs to indicate negation or order.
لا تذهب
Don't go (order)
لا أذهب
I don't go (to school...etc) (negation)
Hope this helps.