Lightroom works with iPad Mini 4, the speed and performance of the app depends upon the size and number of the images you work with, also it depends upon the internet connection speed, how many apps are running in the background.
Also, iPads running Lightroom can capture DNG and HDR images as long as they have 12 megapixel cameras. This essentially means only iPad Pro's can capture DNGs and HDRs in the Lightroom app. This is a hardware requirement, which unfortunately doesn't include the iPad Mini 4. For this and other info, please see the FAQ here: Common questions about Adobe Photoshop Lightroom for mobile and Apple TV