It will spread, and it is not native.
Native alternative to lamb's ear, for the dry full sun location that lambs ear likes and that won't spread aggressively, assuming it is the gray foliage you like:
Field pussytoes (will slowly spread by runners but easy to control):
https://www.prairienursery.com/field-pussytoes-antennaria-neglecta.html?srsltid=AfmBOopF9zw4n4zzLs1t42wVyPGLV-cB9F7IFwsnMUHguAJCkZWV8Zna
Heuchera villosa (while most coral bells like shade, some do well in full sun, particularly darker leaved varieites and hybrids, like ‘Southern Comfort’ and ‘Georgia Peach’ "Caramel," "Tiramisu")
rattlesanke master (intriquing native plant for the mid atlantic, has a southwestern look to it)
Pearly everlasting (a bit taller):
https://www.prairiemoon.com/anaphalis-margaritacea-pearly-everlasting
Silver yarrow (
https://naturesherbfarms.com/silver-yarrow/)
For shade:
Tiarella cordifoloa (foam flower)
Heuchera (coral bells-- many color options including some silvery, e.e. "Stainless Steel, Siler scroll, Silver gumdrop, etc.)
Phlox stolonifera 'White Ridge' (or 'Bruce's White')
Phlox divaricata 'White Perfume'
white wood aster
Non-Natives
If you don't care about it being native, other plants with gray foliage are listed here:
https://www.thespruce.com/pictures-of-silver-foliage-plants-4069719