I have played gragas a lot and I know it's really hard to bully me out of lane, very few champions can outsustain me in lane, and I can build a lot of damage without being as squishy as an oriana would be. But when I do, I tend to be very affraid to bodyslam in because Gragas still has big enough cooldowns to not be able to bodyslam back out before he dies.
I'd say that in the laning phase against gragas you must not try to trade with him, even if you can win the trade (unless the gragas used his abilities to clear the wave, then you have 8 secs to make him pay). That is because of the incredible sustain he has. The champions I've seen do best against my gragas are the ones that outscale me through itemization, like
and sometimes a
or
can attemp to 1v1 me, depending on what he built. Also, tanks do good against gragas if they dont feed through the laning phase.
Now if you're an adc, you have to avoid the bodyslam/ult combo, if you do that, you win the fight. You might want to add a
to your build as a 3rd or 4th item because it's really hard for a gragas (unless he cuts you in the jungle) to break your banshee before ulting. I also suggest you to play high mobility adcs since everything gragas has are skillshots or close-combat abilities. As lucian you can easily dash away from his bodyslam/barel.
and especially
are champions that do really well against the fatty. The trick is not to burn your gap-closer ability before he bodyslams/ults.
Good luck on the rift!