Correct spelling, explanation: luckily is the correct spelling of an adverb formed from an adjective lucky. The general rule is that when we have an adjective ending with a consonant and y, like lucky, to form an adverb we need to change y into i and add the suffix -ly. On that account, we can see that the form luckly is incorrect and the right spelling is luckily.

Definition of luckily:
adverb: for good luck, fortunately;
Luckily, I have brought with me a pair of spare shoes, otherwise, I would be walking around barefoot.
Luckily we were on time, I was afraid that because of that traffic we would miss our train.

Incorrect spelling, explanation: luckly is the incorrect spelling of an adverb luckily. Luckily is formed from the adjective lucky. When there is an adjective ending with a consonant and y, to create an adverb we have to change y into i and add the suffix -ly at the end. For that reason, from lucky we create luckily and not luckly.