You could probably have seen this coming, but personally I think the ineffectiveness of soloing is unique to LoL.
In LoL, you're typically soloing against 1 person, with possible ganks from the jungle across the river, until the mid-game, which, if you're doing well, ganks from anywhere can be expected. As you said, this can be difficult.
In DotA, it's not uncommon for you to be soloing against 2 heroes, sometimes with ganks from a jungle that sits right beside you (not across the river), so in some ways it makes the lane a 3v1. Yet, in DotA this is very possible, and even common in many scenarios.
Consider the situation you're describing: You're a good solo laner, and you're winning your lane. The enemy team notices and starts coming to gank you.
Now there are several key differences between LoL and DotA here:
1. In DotA, wards cover the whole river, so you'll most likely see the enemy team before they come. This gives you more time to react and be prepared than in LoL, where they may just show up and kill you.
2. If the whole enemy team shows up to kill you and take the tower, your team can be there within seconds assuming they have scrolls of teleport.
-This isn't possible in LoL. Teleport is a Summoner Spell, but it's not often taken, and even when it is it has a very long cooldown compared to scroll of teleport. Your teammates may not use it to save you or defend your tower.
3. "Fortify" is a base game mechanic of DotA, so if your tower is under heavy attack, anybody can use it, giving your team 4 more seconds to respond. 4 more seconds means a lot more in DotA than it does in LoL btw, since in LoL most players are going to have to walk there. 4 seconds in DotA means several teammates could have teleported in to help you. Fortify is a Summoner Spell in LoL, but YOU can't control when your teammate uses it, and they may not use it to help you, if they even have it at all.
In other words, the game mechanics in DotA are a lot more friendly for solo laners. If the enemy team realizes you're a good player and comes to shut you down, your team has a way to respond quickly, instead of just letting them kill you and your tower(s).
Of course this doesn't mean that they WILL come help you in DotA, but they at least have the option. The better you get at DotA, you start getting paired with better players, and they tend to help you more because they realize the importance of towers and defending your teammates.
With all that said, I agree with Minotaar that MOBA/ARTS are team games. Regardless of personal skill, your win or loss ultimately depends on your team. However, I like to think that personal skill has a much bigger impact in DotA than it does in LoL, and I think the game mechanics of the two titles reflect that.