Care for liatris
After blooming, should I cut off dead flower?
Rather than a matter of "should you," it's more "what do you want." If you cut off the spent flowers, your plants will look neater, they may be encouraged to flower more and longer, and the leaves and roots will be stronger because they're not expending energy to make seeds. If you don't cut off the flowers, they will go to seed and probably reseed themselves, also you can gather the seeds and give them away or plant more liatris beds. Or you can cut some off, and leave some others (the biggest, strongest, or prettiest ones) to make seed. Up to you.
Here's an article on liatris growing: https://www.gardeningknowhow.com/ornamental/flowers/liatris/liatris-blazing-star.htm