Recall the definition of Lindlar catalyst

Lindlar catalyst is a partially deactivated palladium catalyst used for the selective hydrogenation of alkynes to cis-alkenes.

It is typically: $\text{Pd on } CaCO_3 \text{ or charcoal, poisoned with lead acetate/quinoline}$

So the key idea is: palladium catalyst in a partially deactivated form.

Check each option

Option A: Partially deactivated palladised charcoal

This matches the description of Lindlar catalyst, since Lindlar catalyst is a poisoned/deactivated palladium catalyst.

Hence, A is correct.

Option B: Zinc chloride and HCl

This is Lucas reagent, used in alcohol chemistry, not Lindlar catalyst.

Hence, B is incorrect.

Option C: Sodium and Liquid $NH_3$

This is the dissolving metal reduction system used to convert alkynes to trans-alkenes, not Lindlar catalyst.

Hence, C is incorrect.

Option D: Cold dilute solution of $KMnO_4$

This is Baeyer's reagent, used to test unsaturation and for oxidation, not Lindlar catalyst.

Hence, D is incorrect.

Final answer

The correct option is: $\boxed{A}$

Comparison with stored correct answer

Stored correct answer: A

My derived answer: A

Therefore, they agree.