I have a peatol (tiag) lathe and this is how I would do it.
I have a V block that I made by using a countersink held in the chuck to machine a vee in a block bolted to the cross slide. (clocked in square to the lathe axis)
this means that round bar clamped in it can be cross drilled reasonably accurately.
The only way I have of setting it at an angle is with one of those metal protractors with the thin 6 inch rules.
using a 3/16 slot drill , machine a flat on the bar then drill 1/8 ( or drill and ream with a hand reamer held in a collet/ 4 jaw)
fit , say, a 4 inch length of 1/8 drill rod in the hole , transfer the block to my surface plate i.e a piece of old granite worktop, turn the bar end for end and clock the 1/8 bar parallel.
now repeat for drilling hole in other end.
if it was more important that the holes be parallel to each other then i would file an angular setting block and clamp it to the cross slide and set the block against this.
if your lathe is too big or lacks a tee slotted cross slide for this method, then I'd be looking to bolt a 3/4 or 1 inch square bar in the toolpost (in line with the lathe axis) and drill a 1/2 hole through this. Remove and drill and tap a couple of holes for clamping screws and the rest as above. At least you'll have a graduated compound slide to set the angles!
yours
peter