hi
I have been treating lawns for years and I have not seen your

This means that It is not a "weed" possibly related to the strawberry thus is will only flower briefly in spring not usually enough time between mowing. As it has has taken fancy to your lawn you need to do the following.

To kill it of please follow these following instructions.

Get verdone (garden center) crush the leaves and paint on a strong version of verdone 1 part verdone to 20 parts water. The bruised leaves will help the systemic weedkiller get into the waxy part of the leaf and then into the plant. You may need to do 30% of all the leaves at the same time do not spray as this may catch the lawn which will not take delight in such a strong weed kill.

You will also have to watch the temperatures as weed killers work best in temperatures higher that 8 degrees (midday)

I hope this helps