He keeps sending bills to Lois and she just keeps paying them like an idiot.

Well he did that one time he wanted to catch that gang leader, million dollar joe or something like that

Clark Kent probably draws a salary, but I'm guessing he keeps that legal identity totally separate, with separate ownership of stuff.

But there are ways to make income without another person agreeing to payment:

• Lost, abandoned, or mislaid property may be claimed by the finder as their own in some circumstances.
• Certain types of buried treasure can be claimed by the finder, as well.
• Certain natural resources can be claimed by the people who extract them, especially from land or sea or even space that isn't owned by anyone. For example, the Guano Islands Act authorized explorers to claim islands covered in bird shit on behalf of the United States, and bring back all that valuable bird shit.
• At sea, the law of salvage entities a rescuer to some reward for saving a ship or its cargo. There are other reward systems out there, too, including for tips that get criminals arrested/convicted, whistleblower rewards, etc. Maybe fighting crime can pay through those mechanisms.
• Once he actually has property in hand, Superman can also make it more valuable. Processed lumber is more valuable than raw timber, steel is more valuable than the constituent elements that went into making it. And, uh, he could always start a business and sell the stock.

And you don't need an agreement to receive property as gifts after the fact. He might not charge people for his services, but if he's willing to accept their thanks in the form of something valuable, maybe that's something he can make money off of.

Alternatively, he's just been stealing from Lex Luthor.

Maybe there's a shell company that Clark Kent makes payments to, and then Superman bills it for nonexistent super-services so that he can have some spending money while in costume.

He gets a lot of tips.