Do out-of-date TV sets contain lenses within any factor of their machinery?
By "old-fashioned" are you referring to the cathode ray tube? If so it does not use lenses contained by reference to being competent to focus the picture. Websearch "cathode ray tub how it works" and you'll get a ton of links and illustration.
I dont believe so. I think that they have a really sticky glass.
Really thick glass is a lense, so yes they do. Old TVs (not LCD or Plasma) work by shooting electrons through a Vacuum Tube. Electro-magnets next change the frequency of the electron waves to sort different colors. It is then projected onto the screen that you see when it turns on. This is why magnets label Vacuum Tube TVs look funny.
I beleive an early set be like today's projection TV and used a tube and lenses to project the image to a blind for viewing. Ca: 1940
Philco and companies like Halcrafter made them.