The Mythbuster lamellar armor is around 26 kg (show said the paper armor is "nearly 30 pounds"). It managed to stop a flintlock pistol without serious damage to the armor.
It failed against a Colt Revolver, though the armor makers seemed to think that there is a reasonable chance that the penetration wasn't enough to hurt the wearer.
If the squished white thing in the dent is the bullet, then it's definitely not enough to hurt the wearer. It's a shame we don't know the thickness of the armor, but we do know that the armor weighs around 26 kg so we can extrapolate from that.
This suit is made by the same producer weighing 17 kg for medium sized. The producer says that the armor scales are 1 mm of stainless steel.
Given that the two armors have the same coverage, I would say that the lamellar armor in Mythbusters probably had scales of around 1.5mm thick. Modern stainless steel would probably be of higher quality than medieval armor though.
These two Han armors weigh 16.5 kg and 16.85 kg respectively, excluding the weight of the threads. They both have 1 mm scales as well. Given more or less the same weight as the above armor, with around the same coverage and scale thickness, I really don't think the lamellar lacing contribute significantly to the armor's weight at all:
Mail armor generally performs better than lamellar against sword cuts and spear thrusts and arrows shot from warbows, but against heavy hitters such as halberds and poleaxes and arbalests, it is much worse than lamellar.
Generally speaking, I really doubt that mail is better against piercing than lamellar. The riveted mail tested in the following video is a Viking reproduction with 0.8mm diameter, with alternating punched and riveted rings, metal quality is mild steel rather than iron.
The riveted mail did well against a 45 lb Scythian bow and a 350 lb European crossbow (33.57 joules). But against a modern compound bow of 70 lbs it penetrated through the mail and gambeson by about 4 inches, while the modern crossbow with 185 lbs of draw weight (183 joules) penetrated the mail so thoroughly that it's almost as if the mail wasn't there.
The draw weight and joules came from another video from the same guy (Skallagrim):
This goes along the lines of Alan Williams findings in Knight and the Blast Furnace showing that it takes 80 joules for a bodkin arrow to penetrate riveted mail, and 120 joules to penetrate both riveted mail and padded jack. What's interesting about Alan's test is that he tested two mails. One is a reproduction by Erik Schmid and another is a specimen of 14th century mail gusset. Erik Schmid's reproduction did way better than the Medieval specimen, which should be deducible because gussets tend to be less protective than normal mail that is worn as the primary armor. A blade required more than 200 J to penetrate the reproduction, but only 170 J to penetrate the specimen. A lance required more than 200 J to penetrate the reproduction, but only 140 J to penetrate the specimen. However, an arrowhead required 120 J to penetrate both the specimen and the reproduction [The joules involved here includes penetration of the jack behind the mail]. Thin piercing weapons don't seem to be much affected by the increased protectiveness of mail.
The advantage of mail, is that it is light! Given the same coverage, lamellar armor probably needs to be about around 0.6 mm thick in order to weigh the same as mail. Under this circumstance, the lamellar's protective ability would decrease significantly. So judging lamellar to mail probably isn't very fair, because lamellar weighs more than mail when given the same coverage. For fairness, a person in mail should wear two suits of mail as protection, when pitted against lamellar armor of ~1.2 mm thick scales (given the same metal quality and coverage).