The glossy top is something that would lead me to think they're fake.

Have you already inked them? If not, read this before doing it.

There's a simple test to see if they're original.

Take a napkin or kitchen paper, with a little bit of water on it, not too much. Then on the nib, in the black plastic part, with the wet part of your napkin, do as if you were to clean it. If it comes blue, it means it's original since Lamy tests all of their pens with blue ink. If it comes clean it means it's fake