You have two identical bolts and nuts torqued to the same spec clamping two faces together. One bolt is lubricated while the other is not. What is the clamp load of each bolt?
When you apply a lubricant to a bolt, it reduces the friction in the threads and under the bolt head. This means that for the same torque, a lubricated bolt will have a higher clamp load than a non-lubricated bolt The lubricant allows more of the torque to be converted into clamp load, rather than being lost overcoming friction.
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The relevant equation to calculate the torque-to-preload/clamp load relationship is as follows:
T = F * K * D
Torque = Bolt_Preload_Force * Nut_Factor * Bolt_Major_Diameter
The “nut factor” is a value used to capture various effects in the bolted joint, such as friction in the threads, friction under the head of the bolt, etc. Lookup tables for the K factor are available for nuts and bolts in various conditions, such as different material plating.
In this example problem, changing the lubrication is equivalent to lowering the K factor.
Note that the key takeaway here is that torque is NOT a direct measurement of bolt preload. It is also not a very accurate one - a common rule of thumb is that after applying a certain torque value, you can expect the bolt preload force to vary by +/-25%.
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