Can you help identify this weed?
Weeds are going to appear wherever sunlight hits the soil. So increasing lawn density by proper mowing, watering and fertilizing is the best long term remedy. The particular weed in the center of the photos look a lot like doveweed, or another such weed that is more closely related to Wandering Jew or Dayflower than to grass. The product Celsius (ingredients are thiencarbazone-methyl + iodosulfuron-methyl + dicamba]) does a decent job but may have to be reapplied in time. Follow label instructions very carefully.
Hand removal here and there over time as you build the turf density is also a good option if the infestation is not too extensive.