I have done this. I don't know who would consider it
safe, exactly, and from what I understand the trip was not entirely legal, but nobody got (seriously) hurt and it was an experience I will never forget.
We hiked out to the lava river in the pitch dark, starting off around 2-3 AM, and stayed til it was fully light. We saw a few helicopters after the sun rose but met no other hikers. We had two local guides who had scouted the route the night before.
It was spectacular and surprising, a truly alien environment. For all the hazards, I'd certainly do it again if I ever got the chance.
I went back to Kilauea several years later, on a boat - there were commercial tours which would take you right up to where the lava flow splashed into the sea. I was glad to see it from the other perspective, but walking up to the lava, getting right in there, and poking it with a stick, was by far the more intense experience.