Here is the version of reverse Fatou's lemma I am looking at.
$E_n$ is a sequence of events. $P(\limsup E_n) \geq \limsup P(E_n)$
Here is Fatou's lemma.
Let $f_1,f_2,\ldots$ be a sequence of non-negative measurable functions on a measure space $(S, \Sigma, \mu)$. Define the function $f:S \to [0,1]$ a.e. pointwise limit by :$$f(s) =\liminf_{n\to\infty} f_n(s),\qquad s\in S.$$ Then $f$ is measurable and $$\int_S f\,d\mu \le \liminf_{n\to\infty} \int_S f_n\,d\mu\,.$$
What is the connection of the two theorems?