Just dig up clumps with a generous rootball and store in shade until ready to replant. Plastic grocery bags make excellent storage containers :-) Lightweight, free, easily portable....just make sure there is a drain hole or two in the bag. Water as needed.

I transplant nearly any plant this way. And I hate to admit that sometimes they stay in their temporary bags longer than just a couple of weeks. I have two divisions of plants I dug from my sister's garden over a year ago that are still waiting for a permanent home........and doing just fine in their plastic bags :-)

You can divide them with a hand saw or for bigger clumps I use a electric sawzal. Ive done so much dividing of lirope over the last 5 yrs lol. Its one tough grass. I have several rows like in the picture below.(this is just the back yard summer 2018). If you look at that edge by the evergreen trees, that is now rows of lirope from a recent divide I did. I had to fill that in because its on a slope and water was running down it causing me problems.

Also Lirope blooms small purple flowers late summer. Last summer I never seen it bloom this nice before(forgot to take a pic)

Side note: Lirope makes a great border for bermuda(see below pic)