What is the normalization factor for the quincunx lattice wavelet transform, and how do you find it?
I don't think there is any single best number for normalisation because it depends on the structure of the values in your lattice.

In the simplest case where all values are equal, the predict operation zeros the black points and the update does not change the white points.  Because each  predict-update pair halves the number of nonzero points, multiplying the lattice by sqrt(2) after each pair of steps would conserve energy. 

With all values independent with zero mean and equal variance, the predict step multiplies the variance of the black points by 5/4 and then the update step multiplies the variance of the white points by 281/256 so energy increases at each step.