A weedy Veronica like V. persica or something similar. It had tiny blue flowers last month, now it is going to seed and then the plant will die. The seeds will germinate in the fall and start the cycle over.

It's invading your lawn because there are holes in the lawn, probably from it being too shady. You could try overseeding with a shade tolerant grass or use a pre emergent herbicide late summer, make sure the one you choose will kill Veronica.

I aerate and overseed every few years!

btw, what is a premergent herbicide...Scotts Plus 2 or similar or something your spray.