No, there is plenty of sun light able to hit a majority of the lawn. There are relatively few fir trees in the immediate lawn adjacent to the house. I couldn't imagine the adjacent fir trees having such a drastic impact on the Ph. However, this is where the majority of the moss is concentrated. Also, the immediate lawn slopes away from the house, except for one small area in the back. Also, there is just as much moss in the south facing yard as the north facing yard.
The extended lawn that follows the paved driveway out to the main road has various evergreen and broadleaf trees shading the majority of the grass and there is relatively little moss growing in this area.
I can only assume a few things at this point...
A.) Maybe fill dirt was brought in from another location to elevate the original build site and it has a different makeup than the native soils that are further from the home site, which do not show overly abundant moss growth.
B.) Maybe the immediate lawn was originally sod? Is sod grown in a clay-type soil?