Something not to overlook...many subdivision yards get filled with all
sorts of crap that may or may not reflect what your area's soil is
really like.
My yard, for instance, had 0-18 inches of basically sandy marl thrown on
top to level it off. Your yard could be filled with biologically dead
crap from 18 feet under from some other area.
Your tests should reveal that but adding real topsoil/humus/compost is
never a bad idea.
-Bill

pelirojaroja wrote:
Well, we rototilled several sections of our yard a month or two ago, then
added topsoil (mixed half-and-half with compost or humus), and you should
see the thick crop of earthworms now.

Since your yard is on the small side, I would rototill (make sure it's right
conditions for that -- not too wet or dry), add compost and till that in,
too, and then top dress with compost and plant grass (if that's what you're
aiming for here -- just guessing.) Your grass seed must be *compatible*
with your conditions. This means, from your description, compatible with
shade, probably high heat-tolerant (given where you live), and clay/acidic
soil.

Consider the lime as a temporary fixative -- your lawn is what it is,
pH-wise.

Good luck!