Better to change rim or tyre size to get lower rolling resistance on trekking tyre?
The tire change would have been the biggest change, the ALLTERRAINasaurus is a knobby tire, while the Lugano is a slick road tire. 

Years back I used an ALLTERRAINasaurus and it had to be one of the slowest touring tires I have used in my life. Some earlier versions I later found out also had an incredibly stiff casing making it even less efficient.  

I have also ridden on Lugano as well. It is a slower tire too, kind of like a gatorskin, but no where near as slow as the ALLTERRAINasaurus.

Note that  your pressure could be an additional confounded factor, that said from my experience with both tires I would put money on the the tire change being the culprit. The rear wheel also carries the most weight so will be disproportionately affected by rolling resistance.