I'm not a pro or something like that, i just delidded my first CPU 2 Pages back.
But I think it doesn't matter of you have 1,5mm of LM between IHS and Die or just 0,5mm (no exact numbers, just an example). The thermal conductivity of LM is just that good.
Thermal Paste is a different matter, thinner is better in that case, otherwise The Tim-Paste might act as a Thermal isolator (or kind of a weakness in the Thermalchain)
It IS important to get it to cover the WHOLE gap between Die and IHS.
Since the LM really likes to stick to itself its a good choice to put LM on Die AND IHS, so gets into the gaps inside the Materials pushing the air out.
By putting it only on the Die there may be miniscule Airbubbles trapped between LM and IHS.
So first cover the whole surface by dropping a maybe 2-3mm drop in the middle and smearing it outwards. Dont worry about covering it evenly the LM also spreads a bit like normal Paste, as long as it is enough in the middle. Repeat with the other one. (with the IHS try to only cover the place where the Die is)
When using LM, lapping is only useful if you want to remove either old LM or that Nickelcoating (which has the same or a bit higher thermal conductivity then the LM, so its less of a reason).
If you use Thermal Paste lapping can reduce the miniscule cracks in the Metal, thus greatly enhance contact. But removing the Nickel can make the copper vulnerable to oxidizing.
Ive heard that some IHS's don't have an even surface but are either concave or convex in which lapping can help making an even surface.
Thermal Paste and Liquidmetal are different about that, since LM does go easier into little cracks inside the Metal (thats why it sticks so hard later on).
Well in this regard i can only say glueing shouldnt make a difference in Temperature, but it secures the IHS on the PCB. When installing the CPU the IHS might slip forward when its not glued or move around when moving the Case. That could raise Temperatures since the TIM isnt spread properly anymore if the IHS moves. If the TIM is dry it can even result in air pockets.
All that is more opinion then fact, but i tend to be close to the truth XD
My TIM on the outside of the IHS was Kryonaut not Conductonaut