What is the rated output of your tractor hydraulics?
What is the rated need of the hyd sprayer pump?
I think you will find the pump is using all - and maybe wants more - oil flow than your tractor can deliver.
It is like flushing a toilet & taking a shower at the same time - only one device gets the most flow of water.
In your case you are not really hurting anything(*), but the pump is using up all the hyd flow available. While the pump ios running, it is using all your hyd capacity, and nothing is left for the 3pt lift.
You have to choose which hyd device you want to work at any one time - the pump, or the 3pt. To make the 3pt raise, you'll need to flip off the pump for a short while.
There are flow dividers, something could be rigged up to split your hyd flow to always have some flow to the spray pump and some flow to the 3pt. BUT it does not sound like you have enough hyd flow to bother trying with this, it will not work if you don't have enough hyd flow from your tractor to start with.
What tractor, what hyd pump does it have if there are several options, and what sprayer pump are you using, good hyd experts here could work out the flow you have, ther flow the pump needs, and if there is any fixes available.
In general, it sounds like the sprayer pump is using up everything available, so the only fix is to go to a pto sprayer pump, or turn off the hyd pump when you need to use the 3pt.
(*)If the sprayer pump is using a lot of oil and working hard on a tractor with a small oil supply, if run for a long time it could heat up the oil and cause foaming, heating, and cause some problems along the way.
--->Paul