The empathy of a member of a particular species is determined by a combination of 3+1 separate sets of evolutionary options working together:
0) State awareness options (Theory of Mind, self and other)
1) Signalling options (Flexibility and range of emotion and communication expression)
2) Signal detection options (Track another's gaze direction with your peripheral vision)
3) Signal processing options (Making sense of the set of signals detected)
To empathise fully, both parties need to have matching sets of evolutionary empathic options. To say that autistic people, or men, or lizards have no empathy is probably a little simplistic.
Differing sets of empathic evolutionary options may still be highly compatible. Man and Dog being a good case in point. Where a participant in an exchange expects the other participant to have a different set of empathic evolutionary options then communication can be more 'forgiving'. This is why many autistic people find foreign cultures to be easier, at least for the first few months until our new found foreign friends adjust. We never expect our family pets to tell us we look nice in that dress either.
We hypothesise that training autistic people to clarify to others how the autistic subset of empathic evolutionary options differs from the full set that is enjoyed by those who are considered unremarkable to a psychiatrist may help members of society at large to integrate properly with it's autistic members.
Finally, do not assume that a lack of detection and processing options means lack of signalling options.