Due to multiple learning disabilities not the least of which is dyslexia---I will only post what resonates here. Since feeling empathy and behaving in an empathetic way are subjective and cannot be quantified, I don't see that one can say aspies absolutely lack empathy. Since aspergers is a spectrum from mild to severe to autistic, won't some aspies have a more ability to empathize than others?
Aspies can be capable of feeling empathy yet not know how to express in their behavior. Again, it is subjective. I can think I am being very expressive toward a co-worker who is needing reassurance, yet that coworker keeps insisting that I am withholding the needed reassurance. I give as much as I know how to give, but on her end, she experiences a lack of comfort coming from me. Her subjective experience of the interaction is different from mine; yet I sense her need and try to fill it.
My trying to fill her need is showing empathy. Her dissastisfaction with my attempt is her experience---and subjective.