Unless you're ambushed it is farily easy to avoid Gragas' slow (technically it is Lux's E with slightly slower travel time), E can be sidestepped (though it is problematic sometimes due to his enormous hitbox that should be fixed long time ago). It is hard to do so if he catches you in bad position (zones you with Q near the wall so you have little space of movement) but then it is your fault if he catches you in that position.
His ult has 0,55 seconds travel time regardless of range he throws at so it is plenty of time to use dash/blink ability or sidestep it so it will throw you at another direction or won't touch you at all.
Turret is safe heaven against him if you can play around it. If you position yourself properly he will throw you either at wall or at the turret so you will remain effectively in same position.
AP increases his burst but it has meaningful drawbacks: he is squishy and makes himself vulnerable if he fails his combo, he can't tower dive effectively and jungle invades from assassins/divers hurt him a ton (often ends in his death), he also makes himself lose some tankiness in later stages of the game while dealing little damage even with ludens that he buys.