Step 1: Layers and lubrication.
Graphite has sheets held by weak forces that slide easily, so it lubricates. Statement A is correct.
Step 2: Conduction.
Each carbon keeps one delocalised electron, so graphite conducts. Statement C is correct.
Step 3: Reject the rest.
Carbon in graphite is sp$^2$, not sp, and diamond conducts heat better, so B and D are wrong.
Step 4: Answer.
\[ \boxed{\text{A and C}} \]