The Collaborative International Dictionary of English v.0.48:

Morally \Mor"al*ly\, adv.
   1. In a moral or ethical sense; according to the rules of
      morality.
      [1913 Webster]

            By good, good morally so called, "bonum honestum"
            ought chiefly to be understood.       --South.
      [1913 Webster]

   2. According to moral rules; virtuously. "To live morally."
      --Dryden.
      [1913 Webster]

   3. In moral qualities; in disposition and character; as, one
      who physically and morally endures hardships.
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   4. In a manner calculated to serve as the basis of action;
      according to the usual course of things and human
      judgment; according to reason and probability.
      [1913 Webster]

            It is morally impossible for an hypocrite to keep
            himself long upon his guard.          --L'Estrange.
      [1913 Webster]

WordNet (r) 3.0 (2006):

morally
    adv 1: with respect to moral principles; "morally unjustified"
    2: in a moral manner; "he acted morally under the circumstances"
       [syn: morally, virtuously] [ant: amorally, immorally]