In reading the entry about type xvi swords on this site it seems to say that the purpose of the lenticular portion of the blade is to make it more suitable for cutting than having a diamond cross section for the full length of the blade like an xv. Why was a lenticular cross section considered preferable for cutting? Is it just more robust or is there a difference in ballistic performance?

I can't explain the technical details, but diamond cross-sections have an objectively poorer performance than lenticular blades. A couple of months ago I was cutting against cardboard boxes and comparing various swords. If I recall correctly, my Albion Castellan (Type XVa) cut to a depth of 21 inches with a zornhau (descending diagonal blow). Similar strikes with my Albion Tritonia (Type XIIIb) and Soldat (curved edge messer) cut to depths around 30 and 31 inches or so respectively. I performed the strikes more than once with each sword and had a comparable discrepancy in performance. Obviously, an XVa diamond sword can cleave deeply, but a lenticular blade and curved blade can cut considerably more effectively.

Please bear in mind that not all diamond swords will necessarily cut to a similar depth, and I expect many lenticular blades would not have cut so deeply as my Tritonia. These figures are just to give you an idea of a possible range in the depth of a cut.

There's also the general trend towards thickness or relative thinness in both styles: lenticular blades are similar to hexagonal cross section blades in that respect, with both styles allowing for thinner but still fairly stiff blades, at the cost of increased weight. Stiffer and lighter blades can be made easily by using a diamond or cross section, at the expense of a thicker cross section. I have a few lenticular blades which use a fuller to reduce the weight, and they cut quite well. I also have two XVIIICs, and although they are both diamond cross sectioned, their width imparts stiffness, and thus the blades are fairly thin. Both are able to cut all sorts of medium, at many angles without any issue. Technique also plays into cutting as well though...

Having a diamond or lenticular cross section isn't the most significant factor in determining whether you've got a sword that will cut well or not. Having a blade that's relatively wide, relatively thin and sharp at the section you're impacting with will make a much bigger real world difference. You also have to consider overall weight, weight distribution and length of both the handle and the blade. My A-n-A semi-custom Durer bastard sword has a relatively narrow diamond cross section blade with very little distal taper and it's fairly thick at the weak but it carries much of its width out to the end of the blade and has a relatively long blade and handle for leverage so it actually ends up cutting pretty well. With it I can cut halfway through the cross section of a single tatami mat by using just the point and maybe 1.5 inches of the blade behind it.

It's all about weapon configuration and choosing the right tool for the job. As far as that goes it's important to remember there are actually three ways to wound with the blade and none of them are "more correct" than another. You have slices along the surface, cleaving cuts that bite deeply into or through a target and thrusts. Swords like the XVa are going to be better at slicing and thrusting than they are at cleaving, swords like XIIa's and XIIIa's are going to be better at slicing and cleaving than they are at thrusting.

The two most important things here are edge angle and blade thickness.

More acute edge angles usually improve cutting. Thinner blades usually improve cutting, because thinner blades - all else being the same - usually have more acute edge angles, and there is less resistance to a thinner blade cutting deeply.

For the same weight per unit length of blade, and the same blade width, lenticular section gives a thinner blade, and usually a less acute edge angle. As long as the edge angle is still acute enough, the thinner blade gives improved cutting.