--delete--

This directly opposes the premise of your question of a person being able to heal things that are part of them but not directly themselves though, so what is the point in addressing that? After further consideration I have to admit this might not be the case. Lift's awesomeness may be growing a new viral culture and not restoring the old infection.

At the end of Edgedancer Lift tells Gawx every time she cuts a wart off her toe her awesomeness heals it back. Warts are caused by a viral infection in the skin. I think it's safe to assume this restores the infection as well as the infected cells. So at least awesomeness, if not other investiture, can restore 'life' down to the viral level.

Sureblood's death

"Your next mission is equally important. One of the Unmade seems willing to break from Odium. Our good and that of your Radiant friends align. You will find this Unmade, and you will persuade it to serve the Ghostbloods. Barring that, you will capture it and deliver it to us. Details will be forthcoming." Oathbring Chapter 122, letter from the Ghostbloods stealthily handed to Shallan by Balat right before her wedding. Shallan deduces that the referenced Unmade is Sja-Anat