How does the Lord Stone’s damage reduction work

What does this mean?

It means, you can take out your completely empty Sword of Flaming Flames, kill a bear with it, and now it's got 5% of the bear's soul for the next fight. (note: works for partially filled magic items too)

Does this require you to have an unused soul gem in inventory for it to work

Nope.

and how does it interact with a soul trap weapon?

1. The soul trap weapon casts soul trap on the creature.
2. The creature dies.
3. 5% of the creature's soul is stored to the weapon.
4. 100% of the creature's soul is stored to an empty gem.

Yes, that is 105% of the soul, which is awesome.

If it's a multiplicative stack as others have noted, it should work like this:

Say you have a 40% shield, a 30% chest piece, and a 20% buff...

In a simple additive system, you would have 90% resistance (40% + 30% + 20%). This is a problem because a user could figure out a way to completely mitigate damage and render certain foes permanently harmless, and what fun would that be? Generally systems that use this method implement caps, either hard (user can't score higher than x%) or soft caps (after x%, all bonuses are reduced by y%)

In a multiplicative system the 1st item adds its full value (in this case 40%), but the next item only adds it's bonus onto the un-resisted portion of the damage. This works out as follows: 40% + (30% * 60%) + (20% * 42%) = 66.4% resistance. The result is a much lower effect when stacking items. This kind of system makes large-chunk items more effective than collections of small-chunk items and also guarantees that no one can ever reach 100% resistance, even without the use of maximum-caps.