Liriope - You can prune before it puts out new growth in the spring.
We cannot identify the ornamental grass in the photo. Prune in the spring as soon as you see signs of new growth. Prune back to about several inches from the ground. You did not mention how old the grass is.
Usually older clumps may flop or grow too large for the space or may die out in the center (called a donut hole). There looks like there may be some dieback in the front area. You can remove any dead sections if there is no new growth.
Decide if you want to leave the plant as is or in the future divide into smaller sections and replant when you see signs of new growth.
Is it OK to cut back the liriope now, even though no new growth is showing yet? Or should we wait for new growth to show?
And the same question about mondo grass, which I think is shown in the photo. Ok to cut it back now, or wait until new growth is showing?
Temperatures have been cold and it is okay to wait until you see some new growth before pruning the mondo grass and the liriope.