Spring time is the best time to cut back your Liriope and Crepe Myrtles. You want to do the trimming of liriope in the late winter/ early spring prior to any growth so that you have clean edges of the plant while it grows for the remainder of the season, otherwise if you wait to late the plant will have jagged edges for the season.
In regards to Crepes there is a proper way and an improper way to trim Crepe Myrtles. What I have seen around town is that homeowners and or businesses will chop them off and they look horrible until the new growth emerges. This is referred to as Crepe Murder.
They have these nubs at the tips that look like they have been doing this for years. If properly trimmed a Crepe is beautiful almost sculpture like in a yard. I see this on many commercial accounts because of improper planting of the tree. The owners did not take into account the height of the tree when planting and when it blocks the view of a window or seems obtrusive this seems to be the easy solution. The proper way is to only cut the tips or nothing thicker than a pencil. Also trim dead branches and broken branches. This will allow the tree to breath, for lack of a better word, and grow into a healthier fuller tree.
It is better to not trim if you're going to chop them off in my opinion.