Let the fat, small and tall knight be called K1, K2 and K3.

Let the knight of life, death and the dungeon be called T, F and ?.

K1 says K3 is T. K2 says K3 is F. K3 says K3 is ?.

K1 could not be T, as T wouldn't lie, and K1 says someone else is T.

K3 could not be T, as T wouldn't lie, and K3 says he is not T.

Therefore, K2 must be T. And since he tells the truth, K3 is F, leaving K1 as ?.