If you purchased the game on CD, your license key should be taped to the inside of the box cover.
If you purchased the game as a download from hanakogames.com, you received an email titled "Long Live The Queen (OS version) Product Information", which contained the links to download the installer and your license key, like so:
SAVE THIS EMAIL! It contains important information you will need to download
and play the game.
Your license code is:
If you no longer have this email, please contact support at hanakogames.com and provide as much information as possible about your order (Name and email address it was ordered under, mailing address, etc) and we will try to locate your license key.
Enter your Long Live The Queen license key: