I'm currently studying L3 reflexology and have just been introduced to the principle of cross-reflexes. I understand from my zone charts how one might work on the right hand instead of the right foot, or on the left elbow instead of the left knee, but in the Reflexology Bible by Louise Keet (page 53) these parts of the body are also crossed right to left and vice versa. So one would work on the right elbow instead of the left knee or the left shoulder instead of the right hip, etc. This crossing from right-to-left seems to be completely at odds with the energy lines and seems totally contradictory. Can anyone please shed some light on this?
Well for a start the theory of energy lines in reflexology is very basic and is just a guide to start you off in this healing art.
Energy does crossover, and in terms of health and illness, for example a left hip problem may be associated with a right shoulder problem. I see this sometimes in my own bodywork practice.
Here is a diagram showing an idea in Thai massage that energy does crossover: 
Thai massage have many energy lines in the body and also in Chinese medicine has a similar system. Both these systems show energy lines as curving along the body, unlike reflexology where the lines are very linear. But nature had a tendency to follow curvy pathways and dead straight lines is more of the product of western thinking.
Also don't forget that the right side of the brain controls the nervous system to the left side of the body and vice versa.
Having said that, problems occur just on one side of the body as well.
The skill of a therapist is work out the best treatment protocol for their client.
So in a practical treatment session, if you have a client that has a right shoulder problem and which to work a cross reflex of the hip. Work the hip reflex on both right and left sides, to cover both scenarios.
Thanks RP, that makes a lot of sense. Also from a functional anatomy (gate) perspective one can understand how the functions of opposing limbs work in concert. So that Thai energy diagram makes more sense to me.