The pyramids can not teleport between map regions. If you switch maps a pyramid left on the ground will be returned to a character's inventory, so you do not loose it.
AFAIK you should be able to throw a pyramid the same way you throw any other item, highlight it in the inventory, select Actions, then Throw (rather than 'Drop Item'), use the left stick to select a destination (as long as it is not blocked or out of reach) and hit the button to accept. That works on PC with the controller UI, at least.
