Answer

When a question involves the dynamic of 253 participants (weird large number), you should immediately think about trying out the scenario with a small number of participants so you can understand the dynamic and then extrapolate to 253. So what if you have $n=1$ lion? He eats the steak and falls asleep, he's no longer hungry and doesn't get eaten by anyone - so steak gets eaten.

What if we have 2 lions? Then if anyone eats the steak, he knows the other lion will eat him, so nobody dares to eat the steak (we assume they'd rather stay hungry than get eaten themselves!).

Three lions: If someone dares to eat the steak, will he get eaten? Well we have two lions remaining, considering whether to eat the sleeping third lion. Notice this is equivalent to the two-lion problem, where the sleeping lion is effectively the steak. If one of the two lions eats him, they themselves get eaten by the third lion, so nobody dears to eat the sleeping lion. Since the first lion is intelligent, he knows he'll be safe and proceeds to eat the steak.

Notice the dynamic, if any lion in $n$-lion problem eats the steak, he gets treated the way steak gets treated in $n-1$. So if the streak gets eaten in $n-1$ lion problem, nobdoy dares eat it in $n$ lion problem. This produces alternating results: if steak was eaten in $n-1$, it won't get eaten in $n$ and vice-versa. At $n=1$ we saw the steak gets eaten, so whenever there's an odd number of lions, the steak will also get eaten. 253 is an odd number, so the steak gets eaten.