Generally, armors are considered brigandines regardless if the armoring material (metal, hardened leather, whatever) is attached on the inside or out, or between two layers. An armor is considered to be a lamellar if it is made of overlapping sheets or layers. Therefore, all scale armors are, by definition, a lamellar brigandine. The coat of plates, in its various forms, is also a brigandine. So is the stuff the Hittites were wearing, back when they were fighting the Egyptians in 4000 BC. And the armguards worn by the Japanese samurai, and some of what was used in China. A lot of stuff qualifies as brigandine by definition.
The Asiatic and Byzantine lamellars, on the other hand, were not a brigandine. Nor were the Japanese body armors. The individual armor sections were laced to each other, rather than to a backing material - and any backing materials were purely for ease of use and maintenance and added little or no strength to the design of the armor.
Now, to get down to cases, yes most of the brigandine armors during the Crusades were lighter scale, of the type normally associated with Eastern Europe. The coats of heavier plates, and heavy trauma plates in general, had really not been in style since the Macedonian Empire (who used two-piece brass torso armors, because they were cheaper than more complex designs). They would not re-appear in any number in Europe until the 1300's or so. The true partial plate armors would be later than that, and full plate later still (generally more as a product of tournaments than combat). The reasons for this shift are complex, but the Roman Empire's preference for maille and banded lamellars over the Greek-style single-piece trauma plates probably had something to do with it. On that point, I think everyone would agree.
So to be very specific, to avoid any more issues of definition: This mod contains various types of maille, medium European scale (call it a brigandine, or a lamellar, or both), and the Asiatic lamellars, plus a few miscellaneous lighter armors. All will stand up as being historically accurate. The Byzantine lamellars have not been added, even though they would be in period, either by oversight or because the map does not go that far.
Again, the research was already done when I offered to help with the damage model. It's good, and I will stand up for whoever did it. If you haven't seen the latest version of the mod (currently in beta testing), wait until you do ... I think the historians will be happy.