No, the lake of fire does not really exist. Nothing in your mythology really exists, it is all just stories. Exactly the same as every other mythology throughout human history.
If there was an afterlife, and your lake of fire, the only people there would be christians. For starters few christians live their religion, they just talk about it. Then there all the criminals from deeply religious cultures. And of course the biggest reason, everyone else would be in their own afterlife. Yes that's right, if your afterlife was real everyone's afterlife would be real. So while christians roasted or sat at the feet of their Master, reincarnationists would keep living different lives, and people without religion but with lots of imagination would be gods.