Generally this looks like a broadleaf type of plant mixed in with grass plants. You're in luck! There is a botanical distinction between the two types of plants. Herbicide makers have a product targeted to broadleaf plants and to grassy plants. The one you want is Weed-b-Gon or Weed-b-Gon Chickweed, Clover, and Oxalis Killer. These are spray products, so you do not have to spray the entire lawn. Simply spot spray the individual weeds. These are not soil drench types of products. All you need is a light mist on the leaves. Depending on how fast this weed drops seed, you may need to repeat applications of the herbicide. If you see it come back after dying once, don't fret. Hit it again as soon as practical so it doesn't have time to drop more seed. Once all the seeds are gone, it should be gone.

There are several approaches to lawn management which discourage weeds. Number 1 is grass density. For cool season grasses the time to thicken the lawn with more seed is in the late summer. If you mix Kentucky bluegrass into a fescue or ryegrass lawn, the KBG will tend to keep itself dense and fill in any thin spots that develop. The second way to discourage weeds is to water deeply and infrequently. Most weed seeds need full sun and continual moisture for several days to germinate. If you water every day in the spring, you are almost guaranteed to get some weed seeds to germinate. If you can control the moisture and water only every month or two in the spring, that keeps the weed seeds from 'hatching.' The third way to keep weeds out is to mulch mow at the mower's highest setting. Mulching provides what I call microcover for the seeds to keep the sunlight off. The tall grass provides more shade than short grass to further keep the sunlight off the weed seeds. So by doing what you need to do anyway (watering and mowing), you can help keep weeds from getting started. We have seen reports from people who did what I suggested and completely stopped their neighbor's weed patch from spreading right at the edge of the lawn. So tall fescue with no weeds next to a full crabgrass lawn. It can happen simply from proper watering and mowing.

Looks a bit like creeping charlie or henbit. If you find the centre you should be able to yank it out.

It's a Veronica species. Look out for tiny blue flowers. Perhaps V arvensis but I don't know which ones would be likely in NJ.