Story in the present, something happened in the distant past
Think of your story time window
How much "past" would you need ? A distance of 0.05 AU from the sun is notYou can have a viable, stable orbit for any planet. But that age, but you don't need thatthis "lava planet" to exist there for 6 billion years, for your story to develop in the present. You just need a planet that is 6 billion years old. ButWhen your story itself will gethas a time window of say, thousands of years, where the situation iscan have developed like you describe. Just put an explanation for the current situationit, e.g.
Unfortunate stellar dynamics in the distant past caused this
Something happened a few million years ago. Due to a near-collision with a neighboring planet, your poor dwarf was moved into its current apocalyptic orbit. At first, when the near collision happened, it need not be a mass extinction event: apart from the view, the unusual irregular temperatures and seasons, no one on your planet noticed what had happened, until it got very warm. Nowadays, everything turned into lava and the dwarf planet is approaching its definite end: but your planet could exist for another, say 100 thousand years, before it has evaporated, or spiraled into the sun. Your story will have a lot of time to develop, your lava planet age (and its past) can be maintained.