While Samsung abandoned the Galaxy Tab 7.7 users, folks at XDA have been churning out quality ROMs for this android tablet from quite sometime now. You can now have android lollipop on Galaxy Tab 7.7 by installing this firmware.
You can download the ROM from here and install it using ODIN. Make sure you have TWRP for Galaxy Tab 7.7 pre installed as only then you will be able to flash custom ROMs on your tablet.
This ROM is based on cyanogen mod 12.1 which is basically android 5.1.1 but without gapps. To get those install this package in recovery. The ROM is not rooted and to get root, simply flash SuperSU-24x.zip in recovery. I have installed this on my Samsung tablet and everything is working as it should. The developer notes that he has not tested mobile date for the i815 version but data is definitely working in p6800 3G version.