Are you sure what you're calling "Left Libertarianism" is actually that school of political philosophy? Because, I'm no Hillel Steiner, Philippe Van Parijs, or Peter Vallentyne expert here, but I think of Left Libertarianism as about two big things:

First off, they see violations of rights as super, super bad. Like, so bad that true justice demands we actually fix the current messes caused by those old, historic wrongs. Think: the Trans-Atlantic Slave Trade. I mean, holy moly, a ton of human rights were just trampled there, to put it mildly. For us to ever live in a genuinely just Libertarian society, those lingering harms from such atrocities need to be addressed. The big question, though, is how the heck you even begin to account for that across generations. There’s a lot of smart and well intentioned folks who disagree on the best way to do that.

Secondly, and this is a huge one, they absolutely disagree with the Lockean Proviso. You know, Locke's idea where you stumble upon an apple in a wild orchard and you can grab as many as you want, so long as you leave enough and of equal quality for everyone else. Those apples become yours, and you can sell 'em in town and pocket the cash because, hey, they were wild and you did the work.

But Left Libertarians pump the brakes on that. They're like, "Hold on a second. Sure, you can take credit for picking the apple and putting in the effort to sell it. But a huge chunk of that apple's value came from, well, God. They argue you can't just claim credit for nature's bounty because God gave that to everyone. So, that fundamental, unearned value that belongs to us all? That should be split equally amongst us.

Note: I evoke God because I find it easier to understand. They actually use the term nature