If by leadwort you mean Ceratostigma plumbaginoides, it is not native. It's origin is China.

I like wild strawberries (Fragaria) -- lovely groundcover, takes sun or shade, and edible berries. Particularly pretty when berries and flowers are on the plant at the same time.

Chrysogonum virginianum (Green-and-gold) has performed really well for me, especially in part or dappled shade. It can handle some full sun depending on how moisture retentive your soil is, but it definitely gets a little "sad" and crispy during periods of extreme heat and drought.

The bloom period is quite long as an added bonus, and it spreads pretty rapidly, but it's not overly aggressive and it's pretty easy to "edit out" any clumps of it that spread beyond where you want them.