hi - your pieces are probably 'flashed' - stained red rather than the colour being a glass overlay process .......... such material with a cranberry/ruby stain has formed a staple diet of the tourist trade from c. 1850 to 1950 and possibly still does. You should be able to tell the difference between flashing and overlay depending on the thickness of the colour. I suspect the images are wheel engraved as opposed to etching, and what determines the quality of decoration is probably the detail in the image - the finer the better - the more coarse then less quality.
IMHO these are C20 pieces and intended for the tourist trade, and some indication of age, though not infallible, might be the extent of wear - I would have thought their use might have been more possibly for water rather than lemonade, bearing in mind the probable eastern European origin, but that's just my opinion. C19 pieces are associated with the Biedermeier style, and you're right about Egermann being near the top of the list for these stained pieces - genuine C19 material is likely to be thicker than later pieces, and I'd suggest that 'sets' of such things were a later phenomenon.
My opinion is that you are almost certainly going to draw a blank re attribution and exact origin - unless matching pieces can be found with positive provenance - what was the auction house description when your purchased this set?
May we see a close up picture of the underside of the jug/pitcher and ditto of one of the tumblers please. thanks.