Itemization for carries/assassins when I am ahead, but my team is behind
Solution 1:
It depends on your team!
The opponents also know you're the biggest guy. They will focus you, trying to take you out as quickly as possible to win the fight because once you're gone, your team is massively behind. In the long run, this means your team will lose the game. There is nearly no carry in the game that can truly carry a game on his own, you always need your team's support in some way or another. So the question is actually, what is the general route you want to take from here in order to squeeze out a win?
End the game as quickly as possible. If you're the only one ahead, chances are you're far ahead. You must capitalize on this and press your advantage before their multiple fed carries can take over and get close enough in strength to overwhelm you together. Taking objectives (mainly turrets) becomes very important and has the nice side-effect of getting your team extra gold. But most importantly, it brings the game closer to its end. And you want the game to end while you're still far ahead. To do this, get damage. The more, the better. Gimmicky tricks are worse than raw damage, you main objective is to bring down those turrets and Inhibitors. This is a high risk, high reward kind of approach. You're basically on your own and need to end the game while your team "distracts" theirs. If they have the means to hold turrets and possibly even split push, you will lose.
Level the field. Carrying can also mean helping your team catch up. If you have several item dependant team members just waiting to get gold and catch up to the enemy team, your main objective becomes giving them the opportunity to farm. This includes minions, objectives, jungle creeps and enemy champions, especially ones with bounties. At this point it's important to focus down their main damage dealers and let your team get kills. Don't take the kills, they serve you much less than the rest of your team. Communication is important here, make sure everyone knows they're supposed to "steal" those kills you're preparing for them. If you can use your lead to have your team catch up, you will come out stronger and possibly catch the enemy team off-guard if they think they're still ahead of most of your team. As always, vision is crucial. In this setting, your main goal is to deal damage consistenly so your team can capitalize on it. Taking out 2 targets quickly and then dying to watch your team get destroyed by the remaining 3 champs is bad, you want to last the entire fight or most of it to make sure your team wins it. This is a situation where a defensive item, especially Guardian Angel, becomes very viable. It ensure exactly that, you outlast their damage dealers. It also has the added benefit of making you a much less attractive target. People don't like attacking an opponent with GA. Use this psychological effect to your advantage so you stay in the fight as long as possible and can help your team win the fight and pull ahead as a whole.
Snowball them to hell. Another possible team composition is a support and crowd-control heavy team. If your team is able to either save you from dying or stop them from damaging you altogether, you don't need defenses. Your team is your defense. If they can keep you alive for as long as possible and help you wreck the enemy team with their skills, go for damage and do wreck them. This is especially true if you have few or no other carries on your team that can benefit greatly from a gold boost. In this case, your team needs you to carry them to victory and will do everything to help you do that. It's fine to be a glass cannon if the other team won't ever get close enough to killing you because you have potent tanks, aoe disablers and healers backing you up. In this setting, you need to snowball. Get all the kills, farm like a madman whenever there are no opponents to kill, get the buffs, get the objectives, build more items and rack up as much damage as possible to mow through all 5 of them. If your entire team dies trying to save you, but buys you enough time to get a pentakill doing so, you will be alone. And you're the one doing the damage, so you'll have quite some time to crush their base.
Here's a summary:
- If you have other carries on your team, carry them. Build defensively to last as long as possible and prepare kills for your teammates.
- If you have a super-defensive team, be their glass cannon. Farm, build anti-champion damage and leave keeping you alive to your team while your destroy the other team.
- If your team has neither, end the game quickly. Build anti-building and anti-minion damage to push. Don't bother farming, the longer the game lasts, the more likely you'll lose.
Solution 2:
When you are ahead, if you are a carry or assassin, you need to continue to build damage.
Why? If you manage to catch an out of position enemy, you need to be able to capitalize on this. If you build defensively, there is a better chance that enemy will get away. You also need to continue to be a threat so that it is riskier for them to try to dive/take objectives. If you don't have enough damage, they can simply ignore you and shove harder without risk of dying when at a turret. Also, your team will likely need the damage if there is a good opportunity for a dragon or baron. Say the enemy team goes back and dragon spawns right as they do, you will have the time to clear the dragon very quickly and get back. If you build defensively, you might run the risk of killing it slower. Same with if you get a lucky ace then you will be able to clear the baron quickly enough before they respawn.
How? It is extremely important to be mindful of positioning. You need to be in a spot that will allow you poke or deal damage to an enemy but at the same time not get caught and focused down. While building offensively is riskier, it's also the best chance of pulling a win for your team (only if you are an assassin or carry. Tanks still need to be tanky). Try to get your team to focus on protecting you. If you can keep your damage up and live, you have a chance to win fights. Your team will need to focus on farming awhile and waiting on them to make mistakes or become too aggressive. Warding is still very important, so if you are the only one ahead it might be worth you buying wards to help out. Vision will win you games here because it could potentially help your team catch an enemy out of position or prevent your team from getting baited into killing someone who appears out of position.
TL;DR; Build damage if that is your role. It is riskier but you can mitigate this by helping to ward. Have your team focus on protecting you since you are the largest point of damage on your team.