Lots of questions, I'm afraid. Can you pull back a bit and take another picture of more of the plant? Are those seed heads part of it? I'm still not getting a real sense of scale. Could you measure a leaf? Is the lawn very damp? Is the stem attached under the leaf rather than on the side?

I don't think it's Glechoma hederaceae (Creeping Charlie) unless it's very wet in the picture.

Does this help? I'll take more pictures if need be.

Yes, the lawn and plants were wet.

The leaves are on a tendril, growing out from a 'mother' plant.

floral_UK is right I think; it looks like ground ivy, Glechoma hederacea (syn. Nepeta glechoma; N. hederacea; Calamintha hederacea; Chamaecissos hederaceus, mint family), aka creeping charlie or gill-over-the-ground or alehoof or tunhoof or catsfoot or field balm, and run-away-robin (I am only aware of all these names since I ID-ed same in my lawn recently, and took notes-hope it's right) .
Has small lavender flowers.
Rina

This post was edited by rina_ on Thu, Sep 11, 14 at 14:12

Thank you both. I had seen CC in pictures, but never saw purple flowers coming out of the weeds in my yard. Perhaps they are short-lived, I'll have to pay more attention.

Problem is, it has now spread from the lawn into my flower beds. Does borax hurt perennials? I saw somewhere that borax kills Creeping Charlie.

If it kills creeping charlie, it's almost guaranteed to be lethal to less invasive plants :)

Thanks, that's what I was afraid of..............

rina - I actually said 'I DON'T think it's Glechoma hederaceae (Creeping Charlie) unless it's very wet in the picture.' G hederaceae does not have shiny leaves. However, since it IS wet it may well be that.

If it's Glechoma hederacea, the stems will be square, and the leaves will smell minty when bruised.

It also resembles creeping speedwell, Veronica filiformis (?). I think it would help with ID to see a length of stem by itself, with any flowers or fruit attached, and a ruler or coin for scale.