I purchased LumaFusion using the Galaxy Store, now I want to get LumaFusion on my Chromebook. Do I have to purchase again?

Unfortunately, the purchase of LumaFusion through the Galaxy Store doesn’t allow you to install LumaFusion through the Play Store or visa versa.  Because they are two different stores it would be considered two separate purchases. Purchase LumaFusion using the store that most suites your requirements.

Link to requesting a refund: https://luma-touch.helpscoutdocs.com/article/218-how-do-i-get-a-refund-for-the-open-beta-version-of-lumafusion-on-android-and-chrome-os