Here's my 2c on the whole zest/pith/juice thing, on the basis of my experience as a cook rather than a brewer (expert cook, beginner brewer)
First of all, it's a good idea to leave the pips out - they're a rich source of pectin (which is why you add them to other fruit jams), so you'll end up with a clearer end result without them.
You want the juice.
The zest contains aromatic oils. Now, I'm not an expert but I think there's probably a tradeoff here: if you include the zest and get the oils, you may well reduce the capacity of your brew to form a nice head when poured. On the other hand, the oils smell and taste nice, and will contribute positively to the overall flavour.
The pith is the most interesting one. In almost all food recipes, you'll find injunctions to make sure you don't get any of the pith into the food because it is very bitter. About the only two counter examples I can think of are when you use mixed peel (which is blanched and boiled in sugar), and a well known flourless orange cake where you boil 4 oranges in water for 2 hours, drain them, then blend the lot - zest, pith, flesh, pips and all. In both cases, the pith is processed in boiling water to extract the bitterness before being used.
Now, being beer lovers, hopheads or not, we all have something of a taste for bitter flavours.
(Chinotto is one of my favourite drinks - many people don't like it because it's too bitter. Incidentally, it's another citrus drink.) This suggests to me that you probably do want to include the pith to balance the sweetness of any unfermentable sugars in the mix. Whether you want to include all the pith, or just some of it, I guess experementation would be the key.
Actually that calls to mind a third place where the pith is included in food - marmalade. In that case it is boiled, but the liquid is included. It does reinforce the point about bitterness - many people don't like marmalade because it's too bitter.
I fear I have not added much to help anyone how to brew better lemonade, but it might offer insights to your results.
cheers,
Tom