huge outbreak of spotted spurge

I have a small lawn for the dog.  I currently have a huge outbreak of what I think is spotted spurge.  In some places, you can't even see the lawn!  For a while I was hand digging it out, but there is just too much.  Any suggestions (minus chemicals) would be appreciated.

I wasn't familiar with spotted spurge, and the first thing to do with unwanted plants is 'know your enemy'!

the laid back gardener has lots of good information:

spotted spurge (Euphorbia maculata, formerly known as Chamaesyce maculata), also called spotted euphorbia, spotted sandmat and milk purslane, a low-growing, spreading annual weed

It can grow well in a low growing lawn, especially if the soil is compacted. Unfortunately as an annual, it doesn't make a good lawn alternative, as it will die back leaving a bare patch in winter. Suggestions include - encourage your lawn to grow longer to shade it out, or top dress and reseed the lawn in early autumn (fall) with an inch of compost, the seeds of the spurge don't germinate without light,

The latex extruded when the stems are broken are usually skin irritant, so wear gloves if you are trying to weed it out.

Ooo, just what I was looking for. Thank you so much!!

Spurge is one plant I ignore.  There are many plants that are worse .

I like the suggestion from that link about corn gluten.