There's no mechanism for this. Sure, they could track the referer (if it's even set - Lemmy apps probably wouldn't bother, browsers can decide not to as well)
But then what? They send a bill to the Lemmy site? Which would be your instance, not the one where it was posted... Which you could then laugh off and post for content
What you're describing doesn't exist, otherwise I could start my own host service and spam posts to Reddit and charge them whatever I want. I could even go to my own content
Now, let's say they did want to do something like this. They could send a "not allowed" picture instead of what you asked for if you don't see a valid site. They could then force developers to get a key and proxy the image over from Reddit (if the key leaked, they'd be on the hook, so you'd almost have to do it server-side)
But that's a bunch of effort on both sides, and people would just reupload somewhere else. It might even lead more people off Reddit
I'm thinking you came to this idea from Reddit saying they started hosting themselves to save money. Here's some reasons why that situation is different
First, imgur does have a system to restrict outside links. Certain content requires either to see it on their site or to meet criteria, like a referral header.
Second, lemmy is basically leaching off Reddit's hosting, but does actually have our own image hosting. Imgur was created to serve Reddit - if imgur decided to delete popular Reddit posts, the site would have looked dead. They were already paying imgur for the service
Third, who says Reddit was telling the truth? They've been chasing the IPO for a long time now, so of course they're going to sell every new feature as profitable. In reality, I'm guessing it was a mix of needing something to spend money on to increase their valuation and wanting more control over their content since imgur had grown beyond just serving Reddit