When I first got my little Atlas/Craftsman 6" It came with a lantern post , I thought that I wanted to keep it original and vintage looking as possible . Quickly that turned out to be a real time consuming frustration . You have a jet 1024 , that is a very nice lathe . I would assume you are more into making parts , then vintage . I would say keep the 4 way post , forget about the lantern and get a QCTP (quick change tool post) Here is a good example , although this one I think is too small for your lathe , but you get the picture . Good Luck ! https://littlemachineshop.com/products/product_view.php?ProductID=4083&category=-419988835
I have both 4 way and QCTP for my 13x40 lathe. If I ever find a complete lantern tool post to fit it for cheap I will buy it. They have their issues but will occasionally get in to tight spots that the others won't get close to without a mile of stickout.