You CAN use a liquid metal paste between the IHS and cooler, but there can be problems with that as well. The biggest problem is that liquid metal paste doesn't react well with aluminum, so you need to make sure that NONE of it comes in contact with any aluminum at all. Considering that most air coolers are aluminum with a copper plate on the bottom this can become problematic.
Personally, I would just get a very high quality non-metallic paste to use between the IHS and cooler, but that's just me. If you're certain you can get it right then nothing is better than liquid metal for transferring heat. And you'll certainly have enough left over after a delid. Choice is yours, but if you do it make sure you're not getting any liquid metal on anything other than the IHS and copper on the heatsink.
Lapping is basically sanding the IHS and cooler to remove any imperfections in the surface. Milling grooves on the heatsink and slight curvature on the IHS are normal. Lapping is the process of sanding both down until you get as close to a perfect surface as you can get. Totally flat with no scratches or marks on either surface. Done right it can drop temps by another 5-10C, but it's VERY time consuming to do right. You've got to have the patience to sand away on metal surfaces for hours, and be careful enough to be very precise when you do it.
If you're interested then read this. It's a basic guide but will give you a good idea of what is involved. To do it right you'll need to lap both the IHS and the surface of the cooler that contacts the IHS.