Do I have Liverworts in my Lawn

I have tried the "Search" for Liverworts with no results.

My problem is an unidentified "weed" in the moist side of the Lawn beside a path that I cannot eradicate by weedkillers.
It grows like a miniature clover but green(non flowering) and creeps through the grass and up the side of the path.

It first came to my attention at the top end of my garden by creeping in from under my neighbours hedge and then through small gaps in my fence.
I didn't know any better and just dug it up and and binned it and as my wife uses that area for growing Foliage, I was able to control it with petrol or clearing the soil as weedol only stopped it temporary.

I must have dropped a bit on the path next to the lawn and a few years ago it spread into the lawn.
I cut this out and cleaned the path but it always returns.

My research so far has a product based on "acetic acid" or the Finalsan based on "perlargonic acid" for hard surface and use around trees and ornamental plants.

I cannot say it is a Liverwort as I now know I have some in my pots.

I need a direction to go and hoped that someone can sugest a route, other than digging the area and washing and then putting a black plastic cover on the area.

Thanks for your time.

There are lots of different types of liverworts, have a look on the following:-

http://www.rhs.org.uk/advice/profiles0205/liverworts.asp

or for oxalis try:-

http://www.rhs.org.uk/advice/profiles1005/oxaliscontrol.asp