Safe-lane trilanes either need kills, or at least a carry worth putting all your eggs in one basket for, ideally both.
Lately I've seen a lot of failed tri-lanes - either massively flawed execution (you wonder how they failed to get kills with the skills they had available), or really poor decisions to make one in the first place.
Case in point, I've just played two games as Slark, who I'm trying to learn. He's a good hero, capable of surviving a tough lone solo, although much better with a support who can help him gank.
The first game, the enemy team picked a Phantom Lancer (groan), one of my team picked Axe to jungle, leaving me a long lane solo. As it turned out PL had Nyx Assassin for support (well I suppose it could have been Keeper of the Light!).
The second game, my team decided to tri-lane a Sven (!), when the opposition had picked Anti-Mage and Spectre. Again, left long lane solo, this time against Anti-Mage and Centaur Warrunner .
Now, there's a difference between surviving a long lane solo, and actually being reasonably effective in it. Both these games it was definitely the first - grab a few LS by the tower, don't get killed - that's about the limit to your success unless the opposition are complete muppets. You can't deny much, and you definitely can't get kills.
In the meantime, the enemy hard carry is having a whale of a time - grabbing freefarm (or close) while kicking back on the sofa.
People, please LOOK at these situations before you set them up! What's more important...to have a jungling Axe, or to stop Phantom Lancer freefarming!!? Same with the other - why ensure farm on Sven, while AM fills his boots? It's just dumb and sets you up to lose the game from minute one. I for one don't mind having a tough solo if it benefits the team, but these kinds of play are just benefiting the opposition...
About that Sven versus Anti-Mage part, in that case I usually run an aggressive trilane: I tried a Juggernaut- Rubick- Nyx Assassin lane once, if I remember well, and they had AM and Ogre Magi; we completely destroyed them and the Healing Ward allowed us to push down the tower. In the meantime, Anti-Fun rotated mid and our supports went to gank other lanes or push, so he hadn't had much time to farm.
Otherwise, you can try using one of those annoying solo laners that harass like hell: Dark Seer and especially Clockwerk are good choices.
Proof that Clockwerk works wonders (at ~12 minutes):
Even for a hero like Dark Seer or Broodmother there are hero combinations that make it extremely hazardous to lane up there, or get denies. Even with Ion Shell they can deny your creeps and still get their last hits in, and certainly throw out enough harassment to make it very difficult for you to grab any xp.
Darkseer immediately comes to mind, I'm often winning the lane or making 2/3 heroes leave the lane because of how strong of a lane presence he has. If the enemy team has at least 3 right click heroes or 2 strong right click heroes that include someone like a Tiny/Sven/Medusa/Phantom Lancer, I'll insta-pick him. Another insta-pickable situation is if they have 4/5 melee heroes. He's immune to slows, your early Soul Ring provides enough regen if you're getting harassed, he doesn't even have to be in lane to be effective.
Bounty Hunter is another, it requires the enemy team to really emphasize on using a lot of money for early ward control, and he can last hit from a distance.
I remember even having to run an Undying in the solo lane, and between the Soul Rip and the Tombstone they couldn't take the tower. This requires a more situational event such as the enemy picks having a trilane without any hard CC like a left-click stun.
Lone Druid is another situational, but effective pick.
There's plenty of heroes that can deal with and even ruin these kind of lanes.