before that VMN40ML goes in, worth checking what force the arm will actually put on it, because the two parts are spec'd nearly a gram apart.
the LS580/LT is rated 1.0-1.5g like the rest of AT's p-mounts (AT85EP is the same, 1.25 nominal), and T4P is a fixed force standard - most p-mount arms just apply 1.25g and give you nothing to adjust. the VMN40ML is the stylus off the VM540ML/VM740ML: 1.8-2.2g, 2.0 nominal, compliance 10 x 10-6 cm/dyne at 100hz. so in a fixed T4P arm you'd be running it 0.55g below its own minimum.
not saying it won't play, flavio's done it and it works. it's that the suspension is built to sit where it sits at about 2g. starve it and the cantilever rides high, SRA and VTA go off with it, the damper isn't loaded the way it was meant to be, and a nude microline is about the least forgiving profile going once it starts to mistrack on hot passages. the whole reason to fit that tip is the contact geometry, and the contact geometry is the first thing you lose when it's under force.
good news is the fix came in the box with it - you said the LS580/LT has the 1/2 inch adapter and leads. in a conventional arm with the adapter you can set 2.0g properly and then the combination really is a VM540ML, which is worth the money. it's the fixed 1.25g trackers where i'd stay on something actually designed for 1.25g, and that unused ATN122LP you've already got is exactly that.
if your deck happens to have adjustable VTF then ignore all of the above and just wind it to 2.0.