The appendix of the paper of McPherson et al (1982) (see screenshot below) contains a derivation of the Systematic Component of Variation (SCV). I understand the derivation with exception of the first step. Here are the premises:

$O_i$: observed cases in region i
$E_i$: expected cases in region i
$\lambda_i$: multiplicative factor associated with region i ($O_i=\lambda_i*E_i$)

Now the following assumptions have been made:

$O_i$ is approximately Poisson distributed with mean $\lambda_iE_i$
$\lambda_i$ is considered as a random variable with expected value $1$ and variance $\sigma^2$.

From these the following formula is concluded:

var($O_i$) = $E_i^2\sigma^2$ + $E_i$

I tried to find out how to get the formula by the given premises and assumptions and didn't succeed. Any idea?

Screenshot of McPherson's derivation: