It depends how much you believe Pliny the Elder as a source on the Romans. Here is the text, although it was in Latin. I gave google a chance:

In both cheeks and eyelids man, women are infected daily with paint such a beautiful attempt to dip his eyes. given the nature of this was seen as the cause of many other things of a sort of fence and a barrier projecting against insects meeting or other things accidentally falling into them. sexual excess causes them to drop off, not undeservedly.

Here is an easier to understand translation:

CHAP. 56.—THE HAIR OF THE EYE-LIDS; WHAT ANIMALS ARE WITHOUT THEM. ANIMALS WHICH CAN SEE ON ONE SIDE ONLY. Man has lashes on the eye-lids on either side; and women even make it their daily care to stain them;1 so ardent are they in the pursuit of beauty, that they must even colour their very eyes. It was with another view, however, that Nature had provided the hair of the eyelids—they were to have acted, so to say, as a kind of rampart for the protection of the sight, and as an advanced bulwark against the approach of insects or other objects which might accidentally come in their way. It is not without some reason that it is said that the eye-lashes^2 fall off with those persons who are too much given to venereal pleasures. Of the other animals, the only ones that have eyelashes are those that have hair on the rest of the body as well; but the quadrupeds have them on the upper eyelid only, and the birds on the lower one: the same is the case also with those which have a soft skin, such as the serpent, and those among the quadrupeds that are oviparous, the lizard, for instance. The ostrich is the only one among the birds that, like man, has eyelashes on either side.

1 Kohl is still used in the east for the same purpose.

2 Aristotle says so, Hist. Anim. B. iii. c. 10.

It then looks like Aristotle's Historia Animalium is referenced.