I’m thinking there’s a typo. 1/8 in is about 3mm and 4-5oz leather is 1.5-2mm.
In any case, no the vinyl cutter cannot handle it. The recommend max for the thick material blade is about 12 mil, or 0.3mm. You’d be pushing it to even get 1oz leather through it.
There are attachments to make it possible on some vinyl cutters, but we do not have them and someone would need to do research to see if they work on our model and what parts would be needed. Any consumable components for that setup would be the responsibility of the user to acquire. You’d also need a sturdy adhesive cutting mat as leather is stretchy and stretchy is a recipe for disappointment on the vinyl cutter. Those mats are also consumable.
You can put veg tanned leather on the laser cutter. If you don’t know how it was tanned, assume it was chrome tanned and therefore dangerous to laser.