Would it be possible to get a bigger, higher-resolution picture of it? I'm having trouble even telling whether it's a weed grass or a herbaceous plant from that little photo...

Most all lawn seed mixes I have seen contain some Kentucky Blue Grass, some kind of Fescue, and some Perennial Rye and some even have annual bluegrass. Glyphosates will kill everything it is sprayed on and is considered by the World Health Organization as a potential carcinogen, probably not the best material to use to kill plants. Fescues are fairly wimpy and covering them with an impervious (sunlight proof) covering for a couple of weeks will kill them and allow reseeding right away, something plant poisons may not allow. kimmq is kimmsr

The first one is one of the stilt grasses, and pull right up. Don't let them go to seed ( a little later in the summer) or you'll have a jillion of them. The second one looks like one of the weedy grasses; I would have said that it was nutsedge, which also grows faster than the rest of the lawn, and which is a horrible weed to get rid of, but those blades look flat, not triangular.

Looks like matchweed, Phyla nodiflora, a.k.a. Frog fruit https://hawthornhillwildflowers.blogspot.com/2015/07/matchweedfog-fruit-phyla-nodiflora.html