Correct spelling


Correct spelling, explanation: the base adjective for this adverb is lucky. Because there is a consonant before y we transform y to i when adding a suffix (in this case adverbial suffix -ly. Therefore the correct form of this adverb is luckily. Luckly is incorrect because there is no need to skip this y, it is only changed to I. Luckily is the correct form of this adverb.

Definition of luckily:
adverb, fortunately, fortuitously
I forgot my wallet, but luckily I could pay with my phone.
Luckily I took my umbrella because it was raining heavily in the afternoon.

Incorrect spelling


Incorrect spelling, explanation: luckly is incorrect (and luckily is correct) because the adjective base for this adverb is lucky, so we cannot skip y. Instead, it is transformed to i before adding the suffix (this is because y in lucky is preceded by a consonant). Thus the correct adverb here is luckily.