John Tieney gives lots of New York Times space to Lomborg's idea that we should do nothing about climate change and spend money on other stuff instead. From a legal perspective, the analogy would be developed countries committing a tort against undeveloped ones by imposing climate change harms on them. Lomborg would have the developed countries choose how to provide some kind of benefit to undeveloped countries too, and presumably feel quite good about themselves in the process.
However, the standard legal process doesn't give the guilty party the option of choosing a benefit for the victim - it compensates the victim and lets the victim figure out what to do with the compensation. In that sense I wouldn't have a problem with a carbon tax that transferred money directly to developing countries, except that it is not going to happen, politically.
The other problem is that climate change doesn't have just one impact. It won't just raise sea levels, it will likely increase tropical storm damage and other flooding damage, it will change precipitation patterns, it acidifies the oceans, and reduces biological diversity, and it has these effects for centuries.* Looking at one tiny part of the environmental harm in isolation might give the "so what" reaction that Lomborg has, but because environmental harm has so many impacts, the legal system tends to favor injunctions requiring reversal of the harm instead of monetary compensation.
*Stoat has a nice example I hadn't thought about - on the claim that it's more expensive to reduce emissions than to move development away from coasts, he says "given how valuable beachfront property is, perhaps reducing CO2 might be cheaper." Just another example.