But then the other owners wouldn't have been able to draw the sword since Leez was technically, still the owner. Or is it because of the time travel paradox? Since she first draw it in the past, the very distant past, her ownership of the sword faded/became small and it allowed the others to draw it.

Probably. Ownership of the Sword of Re is probably like Yaksha's heart. It can only exist at one place at one time but since Leez didn't exist, her ownership didn't exist.

Then how can Leez have ownership of it at the same time as God Kubera? Because Kali isn't bound by the law of cause and effect. Leez was only able to meet Kali on Konchez because when Leez met Kali on Konchez she sent her back in time. Without ownership of the Sword of Re, Leez wouldn't have been able to meet Kali or be her pawn, so Kali gave it to her.

It's also weird since the last owner, Tierra Bell, died in N0, the very year when Leez was born, and until N15, the sword remained ownerless. But if I remember it right, Tierra died during the Cataclysm, so that might be a hole in my theory. Or, was Leez born during the Cataclysm?

I don't think we know enough about the timeline of the Cataclysm to say.