Suppose along with independence in each row of a triangular array, it is given that in each row random variables are identically distributed then what Lindeberg and Lyapunov condition reduces to ? This is Billingsley problem.
As far as Lindeberg condition is concerned, I think as $n$ tends to infinity the number of terms in each row will go to infinity. I don't know what to do with Lyapunov's condition. Any hint will be useful.
With notations of Wikipedia, $s_n^2=n$ (assuming WLOG the variance is $1$). Then Lindeberg condition reduces to $$\mathbb E[(X_0-\mathbb E(X_0))^2\chi(|X_0-\mathbb E(X_0)|\gt \varepsilon\sqrt n],$$ which is equivalent to $X_0\in\mathbb L^2$.
Lyapunov's condition is in turn equivalent to $\mathbb E|X_0|^{2+\delta}$ is finite for some positive $\delta$, which is more restrictive.