Since you mention lateral stiffness, you might find Ali Clarkson’s latest video on his ‘rope spoke’ wheel interesting if you have not see it already. ( I should maybe also put this into the thread that discusses this stuff. )
In it he talks to someone who has developed a parametric finite-element bicycle wheel model and done some analysis of steel versus ‘rope’ spokes under vertical, lateral and torsional loads. The lateral-load discussion starts about 26 minutes, but you probably need to watch it all to understand the modelling and loading conditions for the analysis.
As an aside, one interesting thing I took from this video is that spokes fail because of lack of tension and the fatigue that that causes cycling in and out of the zero load condition. So basically it is slack spokes that fail (at the head at least).