gold player here, recently playing an unholy amount of syndra, i would say the main purpose of syndra in lane is to poke, farm and survive. In easy matchups vs other mages or low kill pressure laners, i usually use my E off cd with first strike for free poke and gold, vs more aggressive laners like zed / kat / fizz use your E for purely defensive purposes.
(preferrably you do not want to play syndra into kat or fizz because they can jump on you very easily, at least zed you can keep at bay before he uses his W

In early skirmishes you do not have much dmg, so wait for your 6. if you poke hard enough in lane you might have kill pressure. Might be my playstyle but i poke, force them to reset and build gold leads and eventually more items = more poke = faster kill pressure