Is it forbidden for a grandmother to apply ointment to her grandson's lower back—because he is unable to do so himself—on the grounds that she saw his lower back?

The lower back is considered awrah (private parts) and it is not permissible for anyone other than the wife to touch or look at it, except in cases of medical necessity. Therefore, there is no blame upon you or your grandmother for what she did out of necessity, unless a wife or a man could have performed the action, in which case that would have been preferable. It is permissible to look at the awrah to the extent of the need for necessity, such as for treatment and nursing, as necessities permit prohibitions, and need is considered equivalent to necessity.