2 types of elemental lapis... Weapon slottable and Armour (chestpiece) slottable.
Each element type is strong against 1 other element, and weak against another one, as shown here.
Fire - Strong against Wind - Weak against Water
Water - Strong against Fire - Weak against Earth
Earth - Strong against Water - Weak against Wind
Wind- Strong against Earth - Weak against Fire
ATTACKING
If Barry slots a weapon lapis into his weapon, his total attack is increased by 25% for all attacks, and the weapon takes on the element of choice rather than being non elemental.
This means when he attacks someone using that weapons basic attack (or any skills which arent SET damage) his will attack them with an additional 25% attack power. So if his attack power was 550-600, it becomes 688-750 (this is a non documented increase - the stats screen doesn't show this change)
This is ONLY if the person he is attacking has no armour elemental lapis in his/her chestpiece. However, if they do, a new set of rules applies.
I) If the weapon lapis he has is the element that is STRONG (see above - Strong against) against the element of his opponents armour, he will hit with an attack power of 50% more (instead of 25% more) - so the 550-600 will become 875-900.
II) If the weapon lapis he has is the element that is WEAK (see above - Weakness) against the element of his opponents armour, his attack power will be reduced by 50%. So the 550-600 will become 275-300 when he attacks them.
III) If the weapon lapis he has is NEUTRAL to his opponents armour element (Not strong or weak) his damage will remain the same as if they were both non elemental. He will hit for 550-600.
When I say attack, I also include Magic Missile as being a normal attack, as well as the caster slapping someone with his/her weapon of choice.
ARMOUR
Barry gets himself a nice Armour Lapis. The same rules apply.
If somebody attacks him, and that person has no elemental lapis in his weapon, Barry will take 25% less damage. Same applies for Magic missile if the caster doesn't have an element. Instead of being attacked for 550-600, Barry will be attacked for 413-450.
However if his opponent does have an elemental Lapis in his armour, the 3 rules from above apply once again.
I) If his opponent attacks him with an elemental lapis that is STRONG against Barrys' armour, Barry will suffer an additional 50% attack power on the attack on him, so he will be attacked for 875-900.
II) If his opponent attacks him with an elemental lapis that is WEAK against Barrys' armour, Barry will benefit from a 50% reduction in his opponents attack power. It will decrease to 275-300.
III) If the element of his opponents weapon is NEUTRAL, then the damage done will be normal, and willr emain at 550-600.
IV) As an additional note, if a spell is cast on Barry, then the element of the spell must be taken into account because it is an elemental attack, so you can see what element the spell is and work out from the above how the damage will be affected. Quick example. Fred the mage casts Turbulance and hits for 1000-1200 normally. However, Barry knows Fred lieks Turbulance, and so Barry puts a Fire Lapis in his armour. Wind is weak against fire, so Fred now only hits barry for 500-600 with his Turbulance. However, Fred noticed this massive damage reduction, and thinking fast, he shouts out on vent for Jimmy the priest to quickly cast his water element surge choir at Barry. Jimmy does so, and instead of hitting for 2000-2200, he hits Barry for 3000-3300, because Fire lapised armour is weak against water.
Note, the mage skill Attribute Removal I believe strips your elemental resistance for a time, in other words making your armour into a non-elemental piece for a short while. I've not been online to check this recently tho, so I may have made that up!
Finally, the lapis in your armour and weapon are independant of one another. You can have fire element armour coupled with a water weapon, and you will still hit fire mobs for 50% more, and take 50% reduced damage from wind mobs. They don't cancel one another out. On the other hand, 2 lapises on the same piece of armour or the same weapon does apparently cancel out, and restore the item to non-elemental status.
Hope this kind of explained it all
heh finnaly understand how it works now... 
