Sorry, but I have to correct this because it's a common misunderstanding. It's actually a name collision.
People on the autism spectrum struggle with theory of mind, which is also called "cognitive empathy." We can have difficulty understanding the mental states and emotions of others.
On they other hand, we're often higher than average on what's called "emotional empathy" or "affective empathy." Many autistic people get very distressed when others are unhappy or are suffering. For example, autistic folks are over-represented in the animal rights movements and other movements to reduce suffering.
Somebody who lacks empathy in the everyday use of the word is someone who does not care if others are suffering. That is not a symptom of autism, and never has been going back to the start of research on the topic.