When we hear that someone lacks empathy, most of us automatically think that the person doesn't care about the well-being of anyone else. I used to think the same way, but then I met a close friend who does not experience empathy or emotions the way that a lot of people do, and who does believe that other people's experiences matter. Empathy can be a helpful quality, but a lack of empathy is not a lack of caring.
Empathy is one way to understand someone, but it's not the only way. You can also understand things from a logical, non-emotionally-attached viewpoint that if something is hurting someone, then that thing is a problem and needs to be fixed. The lack of emotional attachment can mean accepting the other person's mindset and not taking into account whether you would feel the same way in that situation. A person who does not experience empathy can care about what other people are going through just as much as someone who is very empathetic.