The scale is the mean of the squared activations over a window of $n = \text{size}$ channels, so $\alpha$ is divided by $n$:

$$y_{i,c,\ldots} = \frac{x_{i,c,\ldots}}{\left(k + \frac{\alpha}{n} \sum_{c'=c-\lfloor n/2 \rfloor}^{c+\lfloor (n-1)/2 \rfloor} x_{i,c',\ldots}^2 \right)^\beta}$$

Channels outside [0, C) count as zero and stay in the denominator $n$. The window reaches size // 2 channels below $c$ and (size - 1) // 2 above it, so for an even size it leans towards the lower channels. This is the reference framework's definition (an average pool of $x^2$ along the channel axis); the AlexNet paper writes the same rule with the $1/n$ folded into $\alpha$. LRN predates BatchNorm and provides only lateral inhibition (no learnt affine), which is why modern architectures usually do not include it.