How do I transition an early lead into finishing a game?
Pace/Tempo is key here. What most people do wrong with their early lead, is to feel secure and slow down, which is the worst thing you can do. Your game has to end before min 30, if you have a lead. Follow up with this list and decide for yourself, what is best at the given moment. Put your focus on executing as much as possible, as fast as possible, since you become the agressor here:
Gank top or bot, trying to force the enemy lane to either die, recall, or end up too low on HP in order to contest the objective you will take straight afterwards.
If possible, take the tower. Optimally, you can get the tower and follow up with dragon/herald afterwards, however mostly times short for both of it. You decide what you go for- infernal or tower, its mostly up to what you think is best. Both can give you more control over the map, thus helping you control more objectives, which then again give you more control. Snowballing itemwise is helpful, but this is snowballing mapcontrolwise, which has a much bigger impact on the outcome of the match. Your teammates can also start roaming around afterwards.
Gank Lanes and shove the wave into the tower, while trying to leave the cs to the laner
Obviously, but mostly when there is no objective you can take, when you cannot get a tower or any other objective, getting a gold advantage for your laners is still better than nothing else. Focus on getting your laner ahead, not entirely yourself. On many ganks, laners lose more gold than they gain, since they often have to sacrifice some CS in order to follow up. Try to leave the kill if possible and when shoving in the wave, try to leave the lasthits.
if you are wide ahead of your enemy jungler as kha and you know kindred should be a piece of cake, make her life harder. Efficient counterjungling requires loads of variables, but keeping the red and blue timer in mind and warding important spots, will make up most of the information you need to understand the jungling pattern of your enemy.
All in all, your biggest enemy when being ahead is time. Time will take your advantage away, being ahead is like a temporary buff, much like baronbuff. If you don't play it efficient, it will cease to exist. Efficiency is Work divided by Time, so make sure you don't wander around putting no pressure onto the enemies. I can assure you there is almost no limit to this. The visibly noticable difference between people, who have 90%+ winrate in gold and actual gold players is almost entirely this efficiency. Once a master player gets fed, he takes complete control over the game and will shut it down faster than you can blink, that should be your goal aswell.
Thats for answering your direct question, however considering you're searching for advice to improve, looking at you overall data, I suggest you focus on the reasons you die. Most of the time it will be situations, that could have been avoided in first place, keep those in mind and make sure you don repeat the same mistakes over and over again. Dying when fed is the best way to make sure your lead is nullified, especially since the bounty rewards make league ridiculously equal-of-outcome economywise, where you can suck however hard you wanna, 1 kill on a 3/0 kha can get you back into the game. Don't forget: 3 solokills on the enemy jungler consecutively get you ~800 gold, if you die afterwards and the enemy team even gets an assist, they get 750 gold. Despite being 3/1 and having completely outplayed your enemy, who only got lucky once, the outcome is not only the same direcly, but indirecly you lose even more, since mostly you're the one sacrificing jungling time, where you could've otherwise cleared camps. Nowadays, playing assassin is sadly all about not dying, rather than "assasinating" others. Killing has become too simple and not dying too important. A good way to start, is to look at how regularly you are aware of the position of everyone else in the game, especially the enemy jungler. Focus on increasing your minimap awareness, aswell as doing research on what information it can give you, but that's another topic, which has millions of good tutorials.