Well, "lucky" is an ADJECTIVE. It's used to qualify a noun. (Generally, a person)
For example, if a person hits the lotto, this individual is "lucky", because it has got all the money alone.
"Is he your boyfriend? Wow, you're so lucky!"
"Luckly is an ADVERB, so you use to it to give a special meaning to any adjective, verb or other abverb.
For example: "I fell down. Luckly, there was a man who helped me up."
I hope it has helped you, even though my explanation was a little confusing =)