4G LTE is a wireless communication standard and not a tablet. As such, users do not download applications for it, but through it. You can download applications by using 4G LTE to connect to your service provider's data network. There are both iOS and Android tablets that support 4G LTE as of 2015.
Apple offers three different lines of iPad tablets as of 2015: iPad Pro, iPad Air and iPad Mini. The iPad Pro is the largest iOS tablet and is best suited for creative professionals. It features a pressure-sensitive stylus that also has two built-in tilt sensors. The harder you press while drawing, the thicker the line is. By tilting the stylus, you can create shading effects by having the stylus act similar to traditional pens and brushes.
Android is a mobile operating system that multiple manufacturers install in their tablets. Some of the available brands are Samsung, Asus, Lenovo and LG. Whether or not an Android tablet supports 4G LTE depends entirely on the individual tablet. The G Pad 7.0 by LG is an Android tablet that has 4G LTE support.
Use the App Store on iOS and the Google Play Store on Android to download applications to your tablet through 4G LTE. Both platforms have free applications as well as paid ones. The App Store requires an Apple account, and the Google Play Store requires a Google account.