Fun almost always leads to increased creativity. If you are enjoying yourself, laughing and smiling, etc. you are more prone to coming up with creative ideas.
Think of it is way, if you’re feeling sad, down or depressed, in a serious mood or doing something that simply isn’t fun then you’re not enjoying the moment and therefore it is going to be highly unlikely for you to come up with something new and inventive.
To promote fun in a work environment, have more casual dress days or the opposite where you dress up as if you’re going to a ball, attempt to turn tasks into team games, have work sessions away from the office, have a day where you dress in costume or invite your team to a pot luck lunch where people all make a course based on a theme.
Fun makes life interesting, so even if you don’t come up with a great creative idea while having fun you will no doubt have enjoyed trying.