It might be. I don't think I have seen burweed here at our place, so I can't be sure. We had it at times in Texas. If it is burweed, it is a cool-season annual that spreads by seeds, so one of the best ways to keep it from spreading is to kill it or remove it before it can set seeds. Then, you either have to hand dig (not pull, because you might leave roots behind) and remove the existing plants or use a herbicide on them. I don't use herbicides, so don't know which ones are labeled for burweed, but surely some of them are.

Often, weeds in lawngrass are a symptom of a bigger problem---that the grass is struggling and not spreading as thickly and densely as it needs to do. A good lawn will shade out/crowd out most weeds, but of course, the problem here is that cool-season weeds germinate, sprout and grow when most lawn grasses are dormant. Sometimes we overseed our lawn in autumn with rye grass (mostly in drought years to give us a protective green envelope around the house as an anti-wildfire measure) and I've noticed that when we do that, the rye grass crowds out all the winter weeds. As a bonus, winter rye grows quickly so we get tons of grass clippings to add to the autumn leaves on the compost pile and on the raised beds. So, if you'd rather avoid using a herbicide, you might sow rye grass seed next fall and see if it will crowd out the burweed. That wouldn't help you right now, but it might help long-term.