It looks quite a bit like knotweed, although the leaves also look a little like a legume. Either way, it appears to be an annual and will soon be dying for this year. If the lawn is thicker next year and gets a good start, the grass will shade and crowd it out. Otherwise, you can use a broadleaf weed killer such as weed n feed or weed b gone when it first begins to show up early next summer.

In the last picture with the bare spot, the plant blooming at the bottom is dutch clover. Very common in lawns and I like it, but it will also be controlled by a broadleaf weed killer if you don't want it.