I would like to thin my liriope and transplant some of it to another area. When is the best time to do this?

Liriope is so incredibly hardy - at least in my part of the world (North Dallas) that the clumps of liriope I tore out of the ground with a grass mattock when I was clearing out a bed in February is STILL thriving in a compost bin - and growing with no sunlight, little water, and temperatures to 160 F.!! Liriope is flowering right now in Dallas, but I don't think that would make it more vulnerable to transplant shock - I don't know where you live, but here I prefer to transplant/divide some perennials in September/October - but with liriope, I think just about anytime except perhaps an ice storm would be all righ!

I agree - you can pretty much transplant liriope anytime - it is very tough.