Should I cut the plant back in the fall?
No, you do not need to cut back Lady's Mantle.
https://www.gardeningknowhow.com/ornamental/flowers/ladys-mantle/grow-ladys-mantle.htm
I have noticed this year that the leaves on my Alchemilla mollis are much bigger than in previous years, indeed bigger than I've seen on the same species elsewhere. No fertilizer applied to their soil. Similarly with a Persicaria, which I took as a chunk from a friend's garden. No fertilizer. Plant twice the height with huge leaves compared to parent plant. Also, an Echinops in a bed which has been given both rotted manure and chicken manure pellets. Why is this happening? Many thanks, jane
The velvety leaves of a Lady's Mantle can reach 6 inches across.
You an improve the looks of the plant by shearing the plant after blooming.
https://www.gardeningknowhow.com/ornamental/flowers/ladys-mantle/grow-ladys-mantle.htm