Garden Grammie, my liriope border is not adjacent to my roses, but I'm responding to the cutting back question. I always mow down my liriope in February (right before the new leaves start growing) to take off the winter-browned part of the foliage. Of course, for you it might need to be done in April(?).

You can use the trimmings to make great compost. Lou

I had a border of the solid green liriope. It became very invasive over time and was choking out the roses, so out it went. My DH had to dig it out which was not an easy task since it had a solid root system. We even had to add in some soil to replace the holes it left when he dug it out. Anyway, I mowed it in the Spring since it always had winter damage just like grass.

The striped liriope never has gotten invasive and stays in nice, neat clumps.

Thanks so much for the response. I was afraid it might try to choke out the roses. Looks like I have some work come this spring. I will definitely add it to my compost heap.