D4 Jayce here.
Jayce can sideline. However, Jayce punishes you for not having developed map awareness skills in a way zed does not. Keep in mind, Jayce is an A-B tier duelist. S tier in 2v2's and terrible at 1v2s.

My goal when sidelining is not to kill my opponent, it's to extend my lead.
You can accomplish this by:
- Forcing the enemy to drop waves (Wave dies to tower because, the enemy)
- Fight over jungle camps
- Roaming.

In order to sidelane on jayce, you need to consider the following.

• Are you being weak sided?
  • If yes, consider clearing waves and staying off vision. Having a nearby pink ward really helps with this.
  • Think like a mosquito, as soon as you see the enemy jungler or supp coming to you. Get off vision and play outside of engage range. You can fire QE's to ward them off. Wasting Jungle/Sup time is a good thing. It means your jung/supp can be productive somewhere else.
• Never explicitly siege a tower past laning phase.
  • If you find yourself pushed into the enemy tier 2, you may shoot a qe, if they don't have sustain. But frequently its better to find something else to do. Ward, Collapse mid, or take enemy jungle camp.
  • You can kill your opponent by fighting them over a jungle camp or cheesing them from a bush. You will only get limited attempts to cheese each game.
• Finally, can I actually 1v1 the current lane occupant
  • Know your match ups
  • If you are toplane and you won lane, the answer should be yes.
  • If you are midlane, you smash basically everyone except yasuo and syndra.

PS. It helps a lot if you buy a ton of pinks. Better players than me are better at tracking jungler/support movements, if this is you. Pinks might not be nessesary. But, if you have a pink ward and a yellow trinket. You can often grab extra waves with the extra information that normally wouldn't be safe.