What are the reqirements or constraints for the crossing lines? Do they have to be perpendicular to one or both lines? Any other guidelines about them?
If it would be good enough you could use perpendicular frames on one of the curves, and intersect CurvePlane with the other curve, then connect the two points (frame center and the intersection point on the other curve). This would guarantee perpendicularity only to one of the curves, though. Etc.
If you upload a gh-file with internalized curves and provide more specific info about the requirements for the crossing lines, then it’s more likely that you get the help you need to solve the problem.