Alright, I admit I was thinking side lanes. So, I've been looking at your match history. Seems like you play a ton of Lux recently, and you have a high amount of Fizz and Annie. So.
Lux: They come out of stealth, get their first hit. Snare, back away, auto attack, luminosity, detonate, auto attack. Throw your shield up in there somewhere. If they're still coming, ult> auto attack. Keep backing towards your tower the whole time.
Fizz: Trickster out. Profit.
Annie: Keep your stun ready. As soon as they jump in, combo burst them into oblivion. Also, you'll find that your stun will make a LOT of people more hesitant to engage.
Eve and Shaco are SUPER squishy. Rengar's probably the hardest matchup there, but considering his invisibility is his ult, you should have yours long before then. Try to pay attention to where he is on the map, and play safe. Example: Stealth champ just ganked top. Stay near the middle of your lane, but for a little bit, you can hover down near the bottom.
If for some ungodly reason, Rengar has maxed out CDR, at level 16 his ult is every 42 seconds. 1) I hope you're out of the laning phase by then. 2) No way in hell is he max CDR. So, for the laning phase ganks, you're looking at, towards the end of the laning phase on superfed rengar, a minimum of 88 seconds between his ults (which is him at level 11 with trinity force and black cleaver because he's murdering everyone and you probably lost the game). MORE LIKELY you're going to be dealing with the FULL 150 seconds between ults (Since the enemy mid is probably getting blue after the first one).
It comes down to awareness. Play like there's a champ that could come out of nowhere at any second to try and murder you. Because there is. Be prepared for them, pay attention to where they are, when they gank, when they use their abilities, etc. Eve even gives you an early warning system :D
Hopefully this helps out.
Also, learn how to deep ward. Mid laners are actually pretty good for it, and it helps out your map awareness a TON. Example: Enemy jungler just ganked top. You have a pink ward in your inventory for this VERY REASON. Do a wave clear (I know you can with lux) to pressure the lane, maybe drop a harass or two on your lane opponent, then go into the enemy bot jungle and drop a well hidden pink ward. Come back to lane and profit.