I have the same problem. We moved into a house with creeping charlie in the lawn. It's at the far side of the yard, and I swear I see it inch closer and close to the house every year.

I heard boron is effective on it you can only use so much before you kill off the grass. I found a paper that suggested a borax, in liquid form, applied at 610g/sq meter was effective at controlling creepy charlie (Hatterman-Valent et al, 1996). While it did damage the grass, the damage to the grass was temporary and lasted only 6 weeks; it will regrow, just the tips of the blades died (Hatterman-Valent et al, 1996).

The solution was made by dissolving the borax in 118g (4oz) of hot water then diluting to 10.2 liter, all of it to be sprayed on one square meter of land in late May or early June (Hatterman-Valent et al, 1996). You should just see the petioles (leaf stalks) and the stems remaining green two weeks after your spraying (Hatterman-Valent et al, 1996). Like applying any kind of chemical, the weather will affect the effectiveness of the borax (Hatterman-Valent et al, 1996). There are tables noting the extent of creeping charlie die back, grass dieback, and temperature data in the original paper, if you are interested in checking it out.

Hatterman-Valenti, H., M.D.K. Owen, and N.E. Christians. 1996. Ground ivy (Glechoma hederacea L.) control in a Kentucky bluegrass turfgrass with Borax. J. Envir. Hort. 14(2):101-104.

Here's something from the Univ. of Guelph
" A more challenging lawn weed control situation is the removal of creeping charlie, bindweed and other creeping weeds from lawns. These weeds don't stand out as individual plants and become intertwined with the grass plants making physical removal or spot spraying with acetic acid virtually impossible. The bad news is that there is really no option to selectively remove these weeds from the lawn. A number of new biologically based herbicides are making their way to the market and may provide some options in the future. At the moment, your best bet would be to insure that your fertility, irrigation and mowing practices are optimized to give the grass a fighting chance in the competition with these weeds. A lawn can still look like a lawn even with a high content of these and other weeds."

Personally, I like to remove the affected patch completely. Rather than spend on chemicals and do all sorts of chemical warfare on the weed. I would rather just remove the patch and reseed the area.

Well it looks like I have a tough battle on my hands.If the area in question was small I would probably remove the Patch and re seed, but unfortunately the CC covers half the Lawn and is heading toward my Flower Beds so whatever I do will have to be done quickly.

in this case, you may need to remove them and resod. There are machines that can do stripping. Barring that you may need to dig the grass out. I did this before using a half moon edger and shovels. Hard work but well worth it.