Incorrect spelling


Incorrect spelling, explanation: this form is incorrect, because the core adjective for this adverb is lucky, so a word that ends with y. This means y (preceded by a consonant) transforms to i when adding a suffix (luckyluckily). It is changed but not skipped, so luckly is incorrect, and the correct form is luckily.

Correct spelling


Correct spelling, explanation: luckily is an adverb. Adverbs are made by adding suffix -ly to adjectives. Adjective lucky ends with y preceded by a consonant, which means, that y transforms to i in case of adding any suffix. Therefore adverb form of lucky is luckily, not lukly (there is no reason to skip y/i).

Definition of luckily:
adverb, in a lucky matter, fortunately
The train was late but luckily we got to the exam on time!
Luckily the weather on holidays was warm and sunny.