Ok, that's much better. Guess it was just the pic that made it look strange.

The hole you are pointing at is for the live center of the lathe when they turn the stub shaft. You won't get any grease to go in there. (that, and, there wouldn't be a point anyway..... anything touching the axle turns with it.)

 

Not impossible but it it is a pita to get to/grease. If you get a 90* zerk fitting and screw that in it's a lot easier. You have to position it with the u joint so you have clearance.

 

I remember when I had the original steering components and the boots were crimped on at their base. No amount of pumping would make grease come out of them unless they were split open and rotten like mine were after getting a little age on them. I got some urethane boots to replace them for a few years and eventually got new steering components.

When you have the front tire off the ground give it a spin and listen for clicking/knocking in those u-joints, that's a sign that they needed grease long ago and now need to be replaced. Grab the axle shaft while you're at it and give a good jiggle to see if it moves in any direction other than spinning, it shouldn't.

 

https://dcjperformance.com/products/spicer_5-3226x
Use these for your axle shafts. The grease fitting is on the end of a cap so you can get at it. This fitting is where you use your needle attachment.