After mowing the lawn again I now realize the importance of mowing at least once a week during a grass's growing cycle. Lightly raking the side of the house turned up a lot of thatch that was extremely long and clearly choking out the grass (this side also had a ton of weeds, go figure). I may need to get something to dethatch it so the live grass will grow thicker.
The grass trimmings can be left in the lawn IF, and only if, you're only cutting a small amount off the top.
The most common grasses also react strongly to being cut, as long as it's only cut a little bit. Mine (Bermuda) gets real fuckin riled up and will spread like mad in retaliation: this is obviously desirable for choking out weeds