that's a pretty ballsy pick there buddy. Melee AD into ryze doesn't exactly work b/c all he does is stack armor and mana. You must be pretty good at Riven
It's a very simple matchup really. You go to lane with a longsword and 3 potions. Ryze can't really kill you he can just harass you so you don't need the dorans blade and you can't spend much time autoing the minion wave for sustain anyways.
Start with your shield or he will beat you level 1 with minion help. Use the brush to your advantage. You just walk up and take last hits and if you see his Q animation you you E to avoid the harass. You can get the melee cs easy but he may be able to deny a couple casters in the first wave. After you have level 2 you can all in him any time he gets close enough to Q you and back off, just make sure his minion wave isn't too large. You'll take a fair amount of damage but with 3 potions you'll heal up and outsustain his 2 biscuits since you do more damage in heavy trades. General rule I use is that you shouldn't go on Ryze unless he has 3 or fewer minions to help fight.
Come back to lane with a brutalizer or pickaxe and pots and collect your free kill at level 6. No ignite necessary. You should have TP. Post 6 Ryze can't fight you, he's extremely weak until he has his ROA stacked. By then you should have the advantage necessary to beat him anyways.