If I am simply swapping out an old LG washer for the same LG washer do I need to buy a new stacking kit or can I use the same one I already have?

Without any model numbers, we cannot determine if the old LG Washer that you are swapping out for what you are referring to as the "same LG Washer" can use the same stacking kit. If by "same LG Washer" you mean that the old washer has the same model number as the one that you are replacing it with, then the same stacking kit that you already have will work. If both the old washer that you are swapping out for the "same LG Washer" have a width of 27", or both have a width of 29", then you can use the same stacking kit that you already have...^IFV