League of Legends (LoL) Question: Keeping a lane advantage?

One of the most important things for pressing an advantage is doing it without being too risky as you mentioned. Therefore, you should only use these strategies when you know the enemy jungler's location or you have warded properly. The following are different ways you can press your advantage:

• Freezing and Zoning. This tactic involves placing your champion behind the enemy caster minions ,last-hitting minions (not pushing), and putting down harass on your enemy if they walk up. This tactic should only be used when your champion can exchange damage better then your opponent.
• Pushing and Roaming. This tactic is probably best for mid-lane but works for others as well. Essentially, you want to push out your lane, and then apply pressure elsewhere on the map whether it's ganking a lane or counter-jungling with your jungler. Additionally, if you see your enemy laner try to follow your roam you can turn on them.
• Buying Items. This probably sounds really stupid, but it's one of the biggest problems that I see every game. If you have the advantage in terms of gold you need to cash it in for items if you want to play like you have an advantage. Items as well as experience are the primary factors of determining whether or not you have an advantage. You should try to buy at the same time as your opponent if not before in order to capitalize on a gold lead.

"Don't be too cocky". That's all guys.

A bit more in-depth:
The fact that you're ahead doesn't mean you can force any engage and come out on top. You can't just blindly jump in as ADC without any direct communcation with your support (or vice versa). You'll have to keep playing the way you did to get the advantage in order to keep it.

It also helps to watch out for the jungler, because the enemy lane will undoubtedly ask for ganks after dying multiple times.

Don't do stupid initiations, don't go 2 v 1 fights, stay behind your peelers, don't use skills stupidly, don't be too cocky

Play by the book OFC. If you are leading, then nothing can undo it but YOUR OWN FAULT. Stick to your strength and punish the enemy when they are trying to get even. Mix in a couple of death sentence for the enemy like early grouping, split push or baron. Winning easy victory is the key to become a good player.

Honestly I love when my Vayne gets ahead. With supreme dueling power once you have Blade of the Ruined King, you could go in 2v1 and sometimes end up with a kill or two.