Source : Webster's Revised Unabridged Dictionary (1913)

Happily \Hap"pi*ly\, adv. [From {Happy}.]
   1. By chance; peradventure; haply. [Obs.] --Piers Plowman.

   2. By good fortune; fortunately; luckily.

            Preferred by conquest, happily o'erthrown. --Waller.

   3. In a happy manner or state; in happy circumstances; as, he
      lived happily with his wife.

   4. With address or dexterity; gracefully; felicitously; in a
      manner to success; with success.

            Formed by thy converse, happily to steer From grave
            to gay, from lively to severe.        --Pope.

   Syn: Fortunately; luckily; successfully; prosperously;
        contentedly; dexterously; felicitously.

Source : WordNet®

happily
     adv 1: in a joyous manner; "they shouted happily" [syn: {merrily},
            {mirthfully}, {gayly}, {blithely}, {jubilantly}, {with
            happiness}] [ant: {unhappily}]
     2: in an unexpectedly lucky way; "happily he was not injured"
        [ant: {sadly}]

Source : Free On-Line Dictionary of Computing

happily
     
        Of software, used to emphasise that a program is unaware of
        some important fact about its environment, either because it
        has been fooled into believing a lie, or because it doesn't
        care.  The sense of "happy" here is not that of elation, but
        rather that of blissful ignorance.  "The program continues to
        run, happily unaware that its output is going to /dev/null."
     
        [{Jargon File}]