From WordNet (r) 2.0 (August 2003) [wn]:
justly
adv 1: with honesty; "he was rightly considered the greatest singer
of his time" [syn: rightly, justifiedly] [ant:
unjustly]
2: in accordance with moral or social standards; "that serves
him right"; "do right by him" [syn: right]
From The Collaborative International Dictionary of English v.0.48 [gcide]:
Justly \Just"ly\, adv. [From Just, a.]
In a just manner; in conformity to law, justice, or
propriety; by right; honestly; fairly; accurately. "In equal
balance justly weighed." --Shak.
[1913 Webster]
Nothing can justly be despised that can not justly be
blamed: where there is no choice there can be no blame.
--South.
[1913 Webster]