The Collaborative International Dictionary of English v.0.48:

Rightly \Right"ly\, adv. [AS. richtlice.]
   1. Straightly; directly; in front. [Obs.] --Shak.
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   2. According to justice; according to the divine will or
      moral rectitude; uprightly; as, duty rightly performed.
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   3. Properly; fitly; suitably; appropriately.
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            Eve rightly called, Mother of all mankind. --Milton.
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   4. According to truth or fact; correctly; not erroneously;
      exactly. "I can not rightly say." --Shak.
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            Thou didst not rightly see.           --Dryden.
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WordNet (r) 3.0 (2006):

rightly
    adv 1: with honesty; "he was rightly considered the greatest
           singer of his time" [syn: rightly, justly,
           justifiedly] [ant: unjustly]