In reality that's not the case, and there is no overarching principle any sect of libertarians hold (as far as I know) that harm can only be addressed via lawsuits. Since the overhead of lawsuits grows ridiculously large when the number of plaintiffs is equal to the population of the country (or even world), the far more practical solution is to just directly apply a Carbon Tax. This is pretty much equivalent to a lawsuit without the overhead of the courts. The biggest difference is while after a lawsuit the wealth is distributed directly, here the wealth is distributed by lowering taxes.
On the other hand I've seen Gary Johnson quotes like this one
> In 2016, as a candidate, Johnson talks about balancing the budget but lacks the zeal of libertarians who think the state could be cut in half without consequence. He’d keep Social Security for current retirees. He wouldn’t abolish the EPA, after learning in New Mexico how the government policed bad actors.
> “In the libertarian view, without the EPA, you as an individual could sue under the law,” said Johnson. “But not really. You don’t have deep pockets to go up against Chevron.”
From: https://www.washingtonpost.com/politics/is-libertarian-gary-...
Either way, good point.
This would be the argument for creating more of a structured market approach to assigning the costs of these externalities: courts are inefficient and plagued with problems when there's a power difference between the parties, so creating a market structure allows those externalities to be compensated in a more efficient way, while still allowing market pricing to incentivize industry to resolve the externality in the most efficient way available.
The libertarian's argument against this (I imagine) is that any government market scheme will screw it up more, though I don't know why so much faith is placed in the court system as a magically efficient system that resolves property disputes fairly and cost effectively in cases like diffused externalities.
But with that said too: the government itself can sue, it doesn't have to be people.
Because no one can own the air and you do not have a right to pollute something you do not own... further more if you pollute on land you do own you cannot guarantee the pollution will go to land owned by other people. And if you can guarantee that it will stay on your property, win win, we solved global warming!