The common blue violets, Viola spp., are a broadleaf perennial that spread by underground stems called rhizomes. It can be somewhat difficult to control, but with correctly timed herbicide applications, you can reduce it with time. Many people choose to leave it in their lawns these days, since it's a native plant that provides benefits to pollinators.

Here's some information regarding control of that plant: https://extension.psu.edu/lawn-and-turfgrass-weeds-wild-violet. Herbicides containing triclopyr have been found to be most effective, but please those that triclopyr damages a broad spectrum of plants including trees and shrubs (although it is selective and shouldn't impact your turf if applied according to the label) and has a longer residual that some other chemicals. 

If all of this sounds like too much to manage, it's okay to turn to a licensed lawn care company to help get your lawn back in better shape.

What to look for in a lawn care provider: https://ohioline.osu.edu/factsheet/hyg-4025-88

Once these issues have been adequately addressed, it should be easier to maintain a more weed-free lawn as long as you provide adequate fertilizer, watering, and keeping your mowing height higher.

The best defense against weeds in the lawn is a healthy stand of turf. Turf is healthiest when mowing heights are kept high, over 3 inches, and when the lawn is adequately fertilized. If you have not done a soil test in the past, I'd highly recommend doing one to address any nutritional issues you may have.

https://www.canr.msu.edu/resources/dont_guess_soil_test_get_your_home_lawn_and_garden_soil_test_kit_today

https://www.canr.msu.edu/resources/mow_high_for_weed_and_grub_control