That is interesting my lathe has a grease zerk on the chuck side and just a hole on the lock nut side.
Guess they are different head stocks.
I tried to grease it but it seems to be plugged. Must have been a few ways to lube these head stocks.
It would not surprise me to disassemble the headstock and find the path blocked. There should be a path- but just knowing how tapered roller bearing races are made it would be hard for where the hole in the casting on my lathe is to end up at the correct place for a clear shot at the outside edge of the race so it can get into the rollers.
I have pulled mower deck spindles apart that had grease zerks that wore out with greasing only to find sealed ball bearings.
Unfortunately My headstock does not have any oil level sight glasses only the change box.