Variables in Stan are default NaNs unless you set them to anything else, so in the block:
model {
matrix[I,J] lambda; // <-- lambda will be NaNs unless you set them equal to something
...
}
target +=gamma_lpdf(lambda[i,j]|alpha[j],beta[j]); or equivalently lambda[i, j] ~ gamma(alpha[j],beta[j]); don’t do any assignment to lambda.
Do you mean for lambda to be a parameter that gets sampled? If so, define it in the parameters block.