I'm planning on buying a new Mac this year (2016) and want to know if I am able to download my purchased LR from Adobe.com. Thank you in advance.
Yes, you can download Lightroom from the following website: Keeping Lightroom Up-to-Date
Be aware that you will need your existing serial number in order to reinstall/activate on a new computer. You might also find the following documents helpful. It outlines the process of moving your Lightroom catalog and images to a new computer: