former adverbial cousin to fast (adj.), from Old English fæstlic "firm, fixed, steadfast, resolute;" obsolete in 19c., simple fast taking its place.
Examples from the Web for fastly
The next day one boy's list began: Slowly, fastly, lily, emily!
Still he sleeps; he will not waken, Fastly closed is his eye; Paler is his cheek, and chiller Than the icy moon on high.The Poetical Works of Henry Kirke White|Henry Kirke White