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]

Moby Thesaurus II by Grady Ward, 1.0:

60 Moby Thesaurus words for "rightly":
   accurately, advantageously, advisably, appropriately, as is proper,
   as is right, by right, by rights, condignly, congruously,
   conveniently, correctly, decently, decorously, deservedly,
   desirably, disinterestedly, dispassionately, duly, equally,
   equitably, evenly, expediently, fair, fairly, faultlessly,
   feasibly, fitly, fittingly, flawlessly, impartially, impersonally,
   in all conscience, in reason, inequity, injustice, just right,
   just so, justifiably, justifiedly, justly, meetly, nicely,
   opportunely, perfectly, practically, properly, right, rightfully,
   seasonably, sic, so, sortably, straight, suitably, to advantage,
   upon even terms, warrantably, warrantedly, without distinction