My answer is actually room 2! (what?) Think about it. In room 1, you will die from the flames or by dehydration, both which are excruciatingly long and painful Deaths. In room 3, as many have stated, the Lions are most likely dead, but then what? Since it is a death penalty, you're not going to get out alive, even if you survive. Thus you will most likely die from malnutrition (that is, if you try surviving on lion meat alone), dehydration,starvation, food poisoning, etc. You get point. As much as the “right” answer is Room 3, it's a death penalty, so you are supposed to die, one way or another. Thus, Room 2 is the safest option as it involves minimal suffering and a relatively fast death.
[okay, maybe I've watched too much Danganronpa, but I'm sure most people would prefer the fast execution over the gruesome ones from the game]
Edit: This is my answer provided that he has to choose a room. Of course, if he chooses not to choose, there's the possibility that someone else will choose instead of him, most likely the judge or possibly the victims relatives (?maybe?), or if chooses to “take an extremely long time deciding" the decision will most likely be made for him instead (again). It has already been decided that it is a death penalty, so there's no escaping it now. All that there is left to hope for is that the assassins make a clean and quick execution.
Alternatively, the assassins may all have been previous murderers who got sent into that room as well and ‘fake’ an execution in order to save him, but that's not likely…