Is it necessary to calculate lane normalisation factor when doing western blot data analysis?
Generally speaking, the proper way to quantify a western blot is to normalize to a loading control such as Actin or GAPDH. In this case it would be (pGSK3/Actin)/(GSK3/Actin) as total GSK3 is not a loading control. A loading control is to protein that is accepted as unvarying in concentration across multiple samples if the same protein amoun is used, and to my knowledge GSK3 would show more biological variability than accepted loading controls. This would be considered the best practice to compare protein concentrations across samples.
That being said, if all you care about is the ratio of active to total, pGSK3/Total GSK3 is probably sufficient to assess if your manipulation changed active/inactive:total ratios. For example, in autophagy assays you can measure autophagic flux by measuring LC3-I to LC3-II, and I've never seen them normalized to a loading control since its a ratiometric readout contained within a single sample.