Yes copper grease should do just fine or any good quality equivalent.
here's how it works, ran a little search and found a pretty good description pasted this from another site,
Fastener Lubrication
It is counter-intuitive to think of using lubricants to keep nuts and bolts from loosening up, but actually it really works!
When you tighten a threaded fastener, you are working against two sorts of resistance:
Actually tightening the fastener by the wedging action of the motion of the slanting threads.
Frictional resistance as the threads slide against one another, and as the bolt head or nut turns against whatever stationary part it presses against.
Only the first of these actually helps hold the parts together. If the threads and head are dry, this frictional force will be the limiting factor in how tight you can get the fastener for a given amount of torque on the wrench.
If you lubricate the threads, and the pushing face of the nut or bolt head, more of your applied wrench torque goes toward actually tightening the fastener.
Lubricating the threads also reduces the risk of stripping the threads.
hope this helps and good luck!!!