Any specific grease to use on front axle?

[Grumpy Goat]

I'm going to be removing the front wheel soon to get a new tire mounted. 

It looks like I'm supposed to coat the front axle with grease. Is a lithium wheel bearing grease fine for that (since I have some). Also, should the nut on the left side be greased? 

Finally, how important is it to do final torque of the axle with the bike on the ground? Thanks.

As TriangleRider mentioned, BMW calls for Optimoly TA grease but that is hard to come by these days and is nothing special. Its just a good grease with molybdenum disulphide in it. This means that, for me, any other grease with that in it would be fine.

When I first removed my front axle for the same reason as you did, it had no obvious grease on it at all. Maybe if I wiped it with parchment paper I might have seen traces of grease. Point is, there was no grease left and the bike or the axle suffered no untoward consequences. Tolerances and material composition are such that the need for grease is probably low to start with, which suggests that perhaps your lithium grease is probably good as well. That said, I bought a tub of heavy duty grease with moly in it and I use that on anything mechanical that needs grease, splines aside. For the front axle I thinly coat the axle with this grease and clean up any excess (not much) scraped off as I push the axle through.

Never grease any nuts.

Finally, torquing the nut with the bike on the ground is safer and more effective. TriangleRider's approach is similar to what I do for mine. In my case I like to tighten the pinch bolts (sequentially) and the axle bolt wrist tight before bouncing the front end so that it self-aligns as needed. After bouncing I then final torque the pinch bolts and the axle. Bouncing while on the centre stand is preferable, in my opinion, since the bike is vertical and the axle is loaded only when you bounce. However, the danger is in rolling forward off the stand. You can assess that risk vs consequences. Taking it off the centre stand to bounce is fine as well.

Although you did not ask, you should also have the bolts for both calipers lightly tightened before bouncing, since you are going to apply the front brake as you bounce. That helps to align the calipers on the discs. Final torquing of the caliper bolts is carefully done with the rest.