The likelihood is implemented in libLSS/physics/likelihood/gaussian.hpp. The class is named LibLSS::GaussianLikelihood.
The statistical model assumes that each voxel is independent. The probability per voxel is {$$ P(N | \lambda, \sigma) = \frac{1}{\sqrt{2\pi}\sigma} \exp\left[-\frac{1}{2\sigma^2}(N - \lambda)^2\right]. $$}