I think the Lyriq is a substantially larger vehicle, almost a foot longer, and a bit wider too than the Mach-E. Also weighs several hundred pounds more across the lineup.
Efficiency in the city is identical at 97 MPGe. Efficiency on the highway is nearly identical with the MME getting 84 MPGe vs the Lyriq's 82 MPGe.
That is such a tiny difference, I'm not even sure it's worth noting really, although any subtle differences are likely due to the larger weight and size of the Lyriq.
Highway efficiency is worse and city is the same. That would indicate that aero has nore to do with the difference than weight Since the city test is much more dynamic in terms of acceleration than the highway test. So the Lyriq is either a bigger brick, or a brick with a poorer profile than the MME.