Can a lense be used in any way, or is it just an item for trading? The description says something like it can be used to see infected particles. Is there any connection with that wierd view-mode you can use by pressing "v" (it shows infected things red-colored, doesn´t it?)?

Yes, the lens is used the prolong the visir use time - you'll find it very useful later in the game, when there are many infected districts.

I used three lenses, now the visir seems to be fully upgraded.

I discovered it shows the places where poisonous clouds will emerge, even if there are none there at the moment.

Playing the translated version, what's visir?

It's an optic device that the Bachelor has. I think you press the 'v' key (by default) to use it. It's very useful as it allows you to see areas of infection in the streets. When you complete certain quests, you gain lenses which can be used to upgrade it.