The most important aspect of polishing the LS range of cars is that basically you are eroding the clearcoat and unless you are very forceful or inexperienced in using a mechanical buffer electric or air you will never polish through to the basecoat colour.
I honed my technique using buffers on yachts (fibreglass) were it is easy to burn the gelcoat running the buffer too fast, you can do the same on a clearcoat laquer and if very careless cut grooves in it.
There will be occasions that some profiles of the bodywork will lose more of the clearcoat surface and create a optical blemish that looks like a drop of water as been squeezed into the surface a bit like silicone spray invading a new paint job but flatter, this is caused by the virtual removal of the clearcoat surface.
I have never used a mechanical buffer on the LS's I have owned ,the only time I see them as appropriate is after a panel respray to polish out blemishes in the spray job.
If you polish by hand it is very unlikely you will do any damage, using a mechanical buffer the damage can be done before you notice it.
If you are intent on using a mechanical buffer use the advice given by Mikeyv keep away from big variable speed buffers such as record ,nutool etc, they will cut the paintwork to shreds.
3M do a great range of compounds and finishing polishes that are mechanical or hand applied.