First of all, it was probably used in the Victorian era (1837 to 1901) as a lemon squeezer and, therefore, a part of the necessary utensils required for afternoon tea. Afternoon tea was founded in 1755 by the Duchess of Bedford who realized she needed some kind of snack in mid-afternoon to tide her over until the evening meal. Whether or not a lemon squeezer was a utensil used then is not known. Since Queen Victoria was all about extreme high social rigor and very proper etiquette, the lemon squeezer was definitely a part of her tea experiences during her reign: 1837 to 1901.
A second use for this utensil is that of a tea bag squeezer. Since the tea bag was not founded until 1908 by American tea importer Thomas Sullivan to ship out his tea samples, we know it could not have been used for that purpose prior to that date and was therefore, not a utensil used by Queen Victoria. Furthermore, since the Victorians created every possible utensil for every possible purpose, it is unlikely the lemon squeezer would have had a dual purpose. They absolutely would have had to create an entirely separate utensil for squeezing tea bags.
I find the list of eating and dining utensils created and used in the Victorian period to be not only fascinating but unbelievable. Here is a list of just some of them: cucumber servers, tomato servers, pickle forks, olive forks, nut shovels and nut serving spoons, asparagus servers, individual asparagus holders, jelly spoons, individual ice cream spoons, forks and knives, fish serving spoons, tea caddy spoons, aspic servers, baked potato forks, marrow scoops, cheese scoops, pastry servers of all types (for breakfast and for teas), salt spoons, bonbon servers and bonbon tongs, sugar sifting spoons, soup spoons, bacon forks, berry spoons, butter knives, individual fish knives and forks, sauce ladles, pate servers, sugar tongs, tea infusers, and tea strainers.
I would not have liked being a dishwasher or silver polisher in that era; I think it could have been a 24-hour job.
The third use of the gizmo could be as a garlic squeezer. Apparently at one time, garlic cloves were served individually to each guest, who then had the option of squeezing their own garlic to the extent of their personal preference.
Cloth and lace doilies: The cloth and lace doilies could also be Victorian. They appear to be about 6 to 8 inches in diameter which means they could have been used as coffee cup or tea cup doilies or as coasters for stemware on top of lace place mats or lace tablecloths.