I was playing with different rom installations last night trying to find the right combination of gapps and lolipop to work on my s3. After some work I finally found the combination.
First off, I am using Liquid Smooth rom the one from sprint at http://drdevs.com/devs/teamliquid/?dir=Nightly/S3_Sprint
Then I had a hard time using some Gapps so it took a while to find one that works but this one worked http://highonandroid.com/android-apps/download-android-5-0-lollipop-gapps/
In Philz recovery, I did a factory wipe for custom rom, flashed the liquid smooth booted in to verify things were working and then flashed GAPPS.
Now I did realize that this didn't ship with root by default so I used the root guide posted to get root installed.
First off, I am using Liquid Smooth rom the one from sprint at http://drdevs.com/devs/teamliquid/?dir=Nightly/S3_Sprint
Then I had a hard time using some Gapps so it took a while to find one that works but this one worked http://highonandroid.com/android-apps/download-android-5-0-lollipop-gapps/
In Philz recovery, I did a factory wipe for custom rom, flashed the liquid smooth booted in to verify things were working and then flashed GAPPS.
Now I did realize that this didn't ship with root by default so I used the root guide posted to get root installed.