1) As luck would have it 2) Auspiciously 3) By good fortune 4) By good luck 5) Favourably 6) Fortuitously 7) Fortunately 8) Happily 9) Mercifully 10) Opportunely 11) Providentially Found on https://www.crosswordclues.com/clue/luckily
Luck'i·ly adverb [ From Lucky .] In a lucky manner; by good fortune; fortunately; -- used in a good sense; as, they luckily escaped injury. Found on http://www.encyclo.co.uk/webster/L/67