lustig: https://dict.leo.org/englisch-deutsch/lustig It has several meanings, the most common are: to be funny, cheerful, making jokes and entertaining people glücklich: https://dict.leo.org/englisch-deutsch/gl%C3%BCcklich He is happy because he is fortunate, successful, lucky to have a nice family, good job etc.

Lustig is funny, glücklich is happy.