Yes both shafts should have the oil hole for the banjo and a second further along the shaft to oil the rocker arm. Look on the drags website here:https://www.draganfly.co.uk/triumph-sho ... _pathway-2
(click on the photo to enlarge it)
I cannot understand how the inlet rocker assembly, fitted with the spindle you say has NO oil feed hole, could have been operating without seizing if its not being lubricated. Are you sure the hole is not just full of gunk?
I think the shafts are hardened so you may have problems drilling it accurately/ easily. I would think someone on the forum will have a spare you can purchase if you need to.
Looking at the diagram above and the parts list no mention of a head gasket. I think there are a few '57 VH owners on the forum, hopefully they will chip in with advise on how to cure your head leak