Help me improve at closing out games

If anyone is really bored and is a high-tier player (preferably Diamond+ but I'll take good advice from anyone) - I recently played a game where I got a huge lead. We did win, although I feel like I should have been able to close it out a lot better. Would love if someone was willing to watch the replay and give me some tips / advice on what I could have done to close it out more solidly (as they won a couple teamfights and while I didn't really ever doubt that we'd win, I don't think with a 12k-15k gold lead we should ever have gotten aced or lost 3+ teamfights in the late game...)

http://www.replay.gg/search/na/valyrianblade#2345767124

It's the 20/7/13 J4 game if the link doesn't highlight for you.

Thanks!