Step 1: Structure of graphite.
Graphite consists of layers of carbon atoms arranged in hexagonal ringsEach carbon atom is sp$^2$-hybridized and bonded to three other carbon atoms forming planar sheets
Step 2: Check hybridization.
Since each carbon atom is sp$^2$ hybridized and not sp hybridized, statement (B) is incorrect
Step 3: Lubricating property.
The layers in graphite are held together by weak van der Waals forcesThese layers can slide over each other easily, giving graphite its lubricating propertyThus, statement (A) is correct
Step 4: Electrical conductivity.
Each carbon atom has one unhybridized p-electron which forms a delocalized $\pi$-electron system across the layersThis allows graphite to conduct electricityThus, statement (C) is correct
Step 5: Thermal conductivity comparison.
Diamond has a three-dimensional covalent network structure, which allows very efficient transfer of heatGraphite has lower thermal conductivity compared to diamondThus, statement (D) is incorrect
Step 6: Summary of correct statements.
Only lubricating property and electrical conductivity are correct characteristics of graphite
Step 7: Conclusion.
\[
\boxed{\text{(A) and (C)}}
\]