In both Finnish and English, 'lasit' can refer to both drinking glasses and spectacles, though when I suggested the latter it was marked as incorrect. I have reported it.
I haven't heard the word "spectacles" since my great-grandfather died. But of course, you're correct. Another possible translation is "eyeglasses."
I think "those" should also be accepted
"those glasses" - nuo lasit, ne lasit (a slight spatial difference between the two Finnish expressions)
"these glasses" - nämä lasit
Why ne instead of he ?
In standard written Finnish, ne is used for animals and things, and he is reserved for people. In colloquial spoken Finnish, ne gets used for people as well as animals and things.