Here's why:
* "Luckily" as an introductory word: If "luckily" starts the sentence, it acts as an introductory phrase. Introductory phrases often need a comma after them.
* Example: Luckily, she had an umbrella.
* "Luckily" as an adverb: If "luckily" modifies a verb within the sentence, it's functioning as an adverb, and you usually don't need a comma.
* Example: She luckily had an umbrella.
Key Takeaway: The placement of the comma depends on the role of "luckily" in the sentence. If it's introducing the sentence, use a comma. If it's modifying a verb, you usually don't.