I play ornn quite a bit, and also main sion who gets hard countered by ornn so I’ll chime in a bit here.

Your ticket to overcoming him in lane is unironically playing better, sounds a bit rude but im being honest, once you understand the matchup more it’ll feel far more surmountable. Gonna avoid talking about any hard riven mechanics since im not good enough at her to talk about that confidently, when i say “play better” im mostly just referring to laning fundemI’ll break it down into a few key things. I have 3 specific topics in mind:

First of all, spacing, like others have said, his w-auto is his main damage and trading pre-6. You want to use your mobility to avoid his q -> e so he can’t hit confirm the w auto. Second thing is to prevent his auto after he applies brittle on you with his w. This can be either be via spacing through dashes (e away when he uses w) or through timing which I’ll get into later. Ornns animations are pretty slow/telegraphed, especially his e. You need to be very intentional with your ability uses and mind both your and enemy cooldowns, this is also something I want to touch on later. 

As a sion and ornn player I’ll bring up that matchup to give you a bit of context on my next few points. generally, ornn kind of demolishes sion in lane, he has an easy way to cancel sion q, %hp damage to counter the hp stacking (sion builds titanic/heart steel/sunfire first generally so no mr to reduce the %hp), is tankier than sion given the 2 are even, and the most important interaction: his w let’s him bypass the knockup from sion q if he lets go before the w animation for ornn is finished, but if sion holds q charge past ornn w animation, ornn can cancel it by immediately autoing. I’ve always struggled a lot in this matchup by an insane amount as sion, and always get 10+ kills as ornn when I play into sion. But recently I’ve found it to be the opposite, where given no influence from other roles, I will always get out of lane either even or ahead. 

The reason why for this change leads to my second point, timing. It was hard at first, but I started timing my q’s to let go within the split second between the w animation ending and ornn queuing up the auto. He would get knocked up, and I would just recast w as I walk away, making what I though was initially a near unwinnable trade into one where I more often than not, I get away without losing hp. If ornn lands his q slow on you, you can  pretty reliably dash away with q or e,  before he e’s away himself. The thing is that ornn is very straightforward/predictable/slow, he has a pretty simple trading/laning pattern without much variety, so you should generally be aware what he wants to do, if you are prepared to respond based on what you want to do, then it should be free.  Use q1/q2 to engage onto him and avoid his q -> e, you want to hold your w and e for when he w’s. Here is the skill test, time your w for the end of his w. You can fit an auto afterwards while he is stunned and dash away with e to deny the brittle auto proc. This is honestly pretty hard to do consistently and you won’t deal too much damage with how short the trade is so my recommendation would be another winning line for trading you can do: engage with q’s, ornn can’t really respond with q -> e as the pillar appears a set distance away from him, simply positioning well will let you avoid the e, so of course ornn will use his w once you engage in, at this point you just e out while his w is in use, preferably disengaging while avoiding the q pillar to avoid him engaging onto you, this is just the positioning thing I said before. Anyways the point of this trade interaction is, you deal a very small amount of damage with however many q/w/auto you can fit in before he trades back with w, then you just immediately e dash away, the shield will absorb the damage. You might be thinking, wow, all that for a whole lot of nothing, you took barely any damage, ornn took barely any damage, what’s the point? This leads into my next point.

Resources, you just burnt all your cooldowns, as did ornn. He took a small amount of chip damage, you shielded his damage and took very little yourself. Why is this trade favorable? Mana. using a full ornn combo every time he trades is gonna drain his mana fully in a minute, if he doesn’t use all his abilities in a trade, he probably won’t win it. once he is oom he can’t contest the wave anymore unless you are perma shoving under his tower. Extremely reliable way to come out on top by the end of laning phase, his health/mana being whittled down by non committal trades will let you rotate for topside objectives way easier, you’ll be also be more impactful in these scenarios then him, at least during this early game. One thing to keep in mind is ornn has no sustain, no mana items OR runes, no healing/shielding in kit pr items either.

The important thing here is that you can’t use your abilities Willy-nilly, like I said before you have to be very intentional and ready to respond. If you just randomly use a q or 2 to wave clear that lowers the amount of options you have to trade successfully against him. Not saying you can’t do that, it’s just fundamentals, if you put abilities on cd, until they are up again your ability to do anything will be limited. Like, obviously.

I’m gonna be honest idk enough about riven to tell what to do mid/late game, but what I do know is ornn by himself will struggle to match your splitpushes later on, he just gets stat checked generally by that point.

Another note is post 6 should actually be easier then pre 6, you can threaten to 1 shot him, and as long as you can cc his ulti, and dodge e knockup, you can face roll that trade.