Hello guys, does anyone knows any textual mention of lamellar or scale armor from those centuries in greece, being used by the byzantine or frankish states soldiers? It seems to me that those kinds of armor appear all the time in the church paintings and even in miniatures, but I still havent seem any written source that mentions it...

I don't think they exist. The vast majority of textual sources don't specify the type of contruction. Most simply use a generic term for armour such as "thorax" or "klibadion". Modern writers can't distinguish between scale and lamellar so there is no chance of an older text doing so.

But is there any evidence for the use of scale or lamellar armor in greece (both by byzantines and frankish crusader states) during those centuries? As far as I've been able to find, the only safe references (that is, not the religious paintings or the Romance of Alexander manuscript), such as the mention by Ibn Battuta of the armor worn by greek cavalrymen or the weapons left by a 14th century soldier to a monastery at Athos about what armor was worn mention only mail and possibly leather armor. Also, the western writers who wrote about the venetian Stradioti (many of whom were greek) only mention a few mails and helmets, other than cloth armor, as being worn by them. Putting those pieces together, I've been inclined to think that lamellar and scale armor were not worn by the late Byzantines or by the majority of greek soldiers after the Latin crusades in greece. That's why I'd like to know if anyone knows of any reference to armor being worn by the late medieval greek soldiers that could be either lamellar or scale...

Well, I haven't looked into it as deeply as you have, but I pretty much share your conclusion (that the evidence doesn't seem to favour the continued use of these types of armour into the time period in question).

There is plenty of evidence for scale armour in Greece from the Bronze Age onwards. There is no evidence for lamellar until after the Roman period. By the 13th-14th centuries they have been pretty much phased out in favour of mail and plate.

Lamellar is mecanicaly waste full, look at all the over lap, that's wasted metal that does nothing towards keeping you safe but you have to carry around.
Plates is per sqare inch/cm lighter and just as good at protecteing you.

Scale and lamellar are usually made from thinner plate. Some are as thin as 0.3mm. The construction relies on the overlap to provide protection. Any attack will meet with two or sometimes three layers of metal. The main problem with these armours is the lacing.

It takes a lot of damage to the lacing before the armour will start to fall apart but the lacing causes lots of other problems. When it gets wet the armour can double in weight and wet lacing can freeze in winter. Blood can't be properly cleaned out, which attracts ants and lice. The lacing deteriorates quickly and has to be replaced regularly. The "plated mail" construction fixed all the problems by replacing lacing with mail.