Makes you wonder how many other vase looking objects should have lids, must be a rare find complete. Wilkinsons own brand glass glue is a couple of quid, it does take some setting though with daylight but gives the chance to adjust to get a good fit and the excess glue cleans great without much effort. I would not use anything else myself, ive found a couple of things recently that have lids and without could be something else.
I wonder if the OP had a purpose other than decorative ?.
It's a good way of checking old damage on glass items as some glue joints glow under UV light, (it might just be uv glue though), I have a lovely old piece of glass that looks mint but in the dark, under UV has been glued twice.