A "lawful" character keeps their word. Abadar is "lawful" because he always tells the truth. Abadar's truthfulness lets people build on top of each other's promises, which keeps them from working at cross purposes and lets them accomplish things that they couldn't alone. "Law" is about organization, and truth is Abadar's organizing principle.
Geryon does not keep his word. Geryon lies, constantly, about everything. Geryon's deceits let him trick people into acting against their interests. "Law" is about organization, and lies are his organizing principle. Geryon counts as "lawful," according to Pharasma, which tells us that while truth can be "lawful," it isn't necessary for "law."
Irori is an ascetic who believes in accomplishing everything with his own power. Irori is Lawful, according to Pharasma. Which tells us that having an organizing principle can be "lawful," but isn't necessary for law. isn't necessary for Law. So it turns out that "law" isn't actually about organization.
What's Law, then? You can lie, "lawfully," you can reject civilization, "lawfully," you can break oaths, "lawfully." And "chaos" is the same way; you can be a "chaotic" muckraker who'd sooner die than bend the truth, you can be a "chaotic" trickster who uses deceit and the trappings of authority to Bavarian Fire Drill your way through life, you can be a "chaotic" mountain man who rejects civilization and lives by his own strength.
The better half of D&D Alignment is just your attitude towards the things you were going to do anyway, half of the other half is your Conscientiousness according to the Big 5, and the rest is just the general impression you give off. "Law" and "chaos" are meaningless as categories and should be relegated to the dustbin of history.