Late Game, Ekko serves the same purpose as any assassin, assassinating squishy targets. The sooner you can do that, the faster you can cripple the enemy's damage output. Anything past that is just cleaning up the team fight (assuming you lived long).
Unless you're ridiculously ahead, assassins are exactly late game powerhouses. They still hurt, but teams usually have methods of dealing with them by then (tanks disrupting, cc lock, niche items like GA or Zhonyas, protecting their late game damage by grouping and peeling) which makes it harder to pick enemies off.
Probably not what you wanted to hear, but you should start looking for ways to close out games sooner, otherwise you lose your advantage window.