Don't restore using titanium backup...
All apps that you backed up, were running on dalvik. When coming to lolipop from any ROM KitKat or below, you can't use titanium back up to restore. You'll have to download the new updated apks from play store that support ART.
Lollipop runs on ART by default. Anything below kitkat runs on Dalvik so to use the rom Without any issues don't restore....
Try using the rom with fresh installation of apps from play store. Might just help
Does that mean that there is no way to transfer app data from stock ROM to Lollipop?