So the objective is to minimize the thermal resistance. Aluminum is a fairly good conductor, but is not as good of a conductor as not having the aluminum there at all. My point - if you use high quality thermal paste and get the heat sink and SSR squarely mounted to the aluminum lid, it shouldn't be a big deal. Done right, there's a chance that the lid acts as part of the heat sink as well, though it will radiate heat back into the box, too.
Personally - I'd use the plastic lid and mount the SSR directly to the heatsink.