The message about needing WiFi is because your device is not connecting to content servers. Make sure you have Internet access by using a browser to see if it downloads content from a web page. Having WiFi, or connection to your local network, is not the same as connecting to the WAN, or the Internet.
Another issue, and probably the case with your device, is lack of support for GL on Android 4.4.4. The current version of Gospel Library is 5.11.3 and may not be supported on Android 4.4.4. Some devices running Android 4.4 do not run TLS 1.2. This is a security protocol required to run GL 5.5 and later. Without TLS 1.2 your device will not be allowed to connect to the content servers. See if your device can be upgraded to Android 5.0 or later. Android 5.0 and later run TLS 1.2.
JD Lessley
Have you tried finding your answer on the ChurchofJesusChrist.org Help Center or Tech Wiki?