Separate from the on/off setting for screen rotation, my device (maybe yours too?) has checkbox's for rotation angles. Maybe yours has 0° as the only mode check'd-in?
Settings > Device > Display:
View attachment 159060
Why don't I have these options? Note3 att I can only toggle rotation on off
Posted via Android Central App
I have ATT Lollipop on my Note 3 and I also only have the checkbox for "auto rotat screen". The is the 2nd time my phone stopped rotating, despite the option being checked. The first time I solved it by: "I cleared all app-cach, powered off, removed battery, booted to recovery mode, cleared system cache, went into settings, unchecked auto rotate, went out of settings, went back in, and now it's working!"