Just because it is possible to lube the splines does not mean that it is the best way to do this job. This is also your first time doing a spline lube? It is good advice, I think, to take the trans out. It will generally be easier to work on stuff and see what is going on. I have done this job many times over the years. I still take the trans out. Did it once by pulling the trans back, once, never again.
Careful not to over lube the spline. The Honda Moly 60 is the product to use. Grease goes only on the input shaft splines. A light coat as said by others.
The idea of sealing the neutral switch is that this switch is an Aluminum casting with a plastic internal portion. There are electric terminals in the plastic. Since you are going to try and seal a switch that already leaks you will have to get the part that is leaking CLEAN. The plastic part is not bonded to the Aluminum or electrical contacts part. So a thin epoxy is used to seal this. It may work if you get it clean enough. If you find other threads here on this subject you may see the pictures of riders epoxy work on these switches. Cool stuff by some of the inmates. If you find that thread post the link, I'd like to see those again. Works of art.