LotR -- Book 3 - Chapter 05 - The White Rider

[HerenIstarion]

Originally Posted by Estelyn Telcontar

do you think what she says about laying his axe to the right tree has a meaning that is important to the plot

If I were a Freudian... but luckily, I'm not one

Hence, I believe it is just a general piece of advice and, at the same time, expression of special sympathy Galadriel has for the dwarf. It almost feels like she's doing her [kind of] duty towards Legolas and Aragorn - the former as a neighbouring elven Kindgom's ruling house member, the latter as kinsman and future son-in-law (and important political entity, or showing promise of becoming one in the future).

With Gimli, on the other hand, it feels like she simply likes the chap, as an interesting, a bit strange, curious, and above all, cute person. Something like a flirt, but Eru forbid think otherwise, innocent flirt. A mother too? Or as an aunty with grown-up children may have special affection for a younger nephew. Galadriel is almost always very lofty, goddess-like (even in her temptations). I reckon Gimli is a medium to show us she's a woman as well, however unwomanlike she may seem (despite her beauty, or even bacuase of her beauty) at times.