Can a union monster equip itself to a monster while LADD is on the field?
ex) Spirit of the Six Samurai equipping itself to Grandmaster

No. Since the Union monster's effect is an ignition effect, LaDD will immediately jump in and negate the activation. Since you have already attempted to activate the effect, you've used up the "once per turn" option it has.

What about the un-equipping of the union monster?

I'm not 100% sure on this one at the moment. My initial thought tells me that yes, LaDD will negate the "unequipping" as well, but I'm trying to recall all the mechanics I know about Union Monsters and Equip Spell cards to see if the unequipping effect would be considered part of a "continuous spell" effect, which cannot be negated.

I'm making the assumption that the Union Monster turn into an equip spell card during the process, since it's text is similar to Dark Necrofear.

Anybody else care to chime in?