It does not look like jade. It does look like fluorite. It doesn’t seem possible that fluorite of this size could be carved with the details that this piece has. Fluorite would have fallen apart. It looks like dyed quartize which is a common and effective and cheaper jade alternative.
I would check its Moh’s hardness. Fluorite will be 4, and will be scratched easily by steel which is 5.5. Maybe also check if you can scratch it with a copper coin which will be 3.5. If it less than that then maybe calcite or a softer mineral alabaster/gypsum.
Fluorite (and calcite) will also fluoresce with UV light. It can occur in a huge range of colours and usually has a cubic habit so maybe look for that. I can’t tell if your lamp is carved or not which may have obliterated any crystal form. If it is fluorite it could be valuable as it is prized by mineral collectors.
Jade will be relatively hard at 6 to 7, which will be close to quartz at 7. So neither will be scratched by steel.
This is fluorite you can tell by the distinctive yellow tone within the material that comes from oxidisation of the exposed matrix of the gem material. it is however advised to do the scratch test in a non visible or viewable position. The matrix of fluorite is not very sound meaning that it is a very fragile sub gem and will scratch very easily so try that and if no scratches appear from lightly scratching with a coin or tea spoon then it could be that it has been film overlayed for extra hold and protection, but it can’t be a dyed quartz as the colour is to deeply saturated throughout the material for it to have been dyed.