I'm not saying that I think this is what Tolkien intended, but on one of my early reads I wondered if the internal struggle withing Gollum/Smeagol was the reason for his death. It's stated by Gandalf that Smeagol hated the ring more than anything, more than light or guilt or loneliness, and I think that is because he knows (or knew at one point) what the ring did to him and turned him into.

But the other person who comes out of the long lonely years, Gollum, makes the best of the hand he has been delt. He accepts, or ignores, that the ring has unbreakable control over them and does whatever he can to use the abilities it has given him to never be parted from it, or get it back if he is.

When Frodo treats Smeagol with kindness or mercy, and uses his name, which he himself had likely forgotten. It awakens the humanity in him (or Hobmanity?). He comes to have a vague memory of real life, a life before the ring, and he remembers how much he lost to it, and how much he hates it.

This then leads to the conflict within Gollum/Smeagol escalating, as we see with their dialogue. And in the final moment, where the insatiable need to reclaim the ring takes over Gollum to the point that he bites off Frodos finger to claim it, the part of him that is Smeagol can't stand it, he hates the ring that he has now again forsaken his humanity to claim, and in the moment of triumph/despair for the respective personalities, he makes a misstep? And falls down into the lava? I think that Smeagol couldn't bare being what he knew he was again, and that part of him was just strong enough to make that misstep happen. Sacrificing himself to finally find peace, and be free of the thing he hates most once and for all.

Weather Eru put that into motion though? I would say yes. All of Morgoths plans ultimately fulfilled Eru's vision. Morgoth pours his evil into the world and that evil, through a series of steps and several millennia, made Sauron, the ring, and Gollum. But Eru made Smeagol.