5 easy steps to avoid being cheesed by Ekko:
Step 1: If you can't kill him twice (or 1 and a half times with ignite/grievous wounds), don't plan on killing him then getting out, because his ult will heal him
Step 2: While you are all inning him as a melee, attack then move, then attack etc... to avoid being on top of his ult
Step 3: When you get a 3 second warning on where his W is, get out of it.
Step 4: His passive is like Diana's passive, and he usually builds lich bane. So his E-Passive proc is going to deal most of his burst damage. Be careful when his passive count gets high. (Avoiding his Q to avoid a double stack is very helpful)
Step 5: The most obvious and the most commonly cited: Don't stand on his ult! The ability is basically a 4 second slow Veigar ult skillshot that you get to see coming. If Veigar's ult became an extremely slow skillshot (Rito pls, this isn't a suggestion. The little guy has been through enough :'( ), you would be a fool to choose not to dodge it.
I see a decent amount of counterplay in his kit, having played against him (and as him) a LOT since release Hope this helps, have a good/better/THEBEST day