Originally Posted by Unca_Sam

You seem really confused.
The purpose of lubricating an IGH is to lubricate the internals parts to minimize wear. ATF is meant to cool and lubricate parts that are much more stressed than an IGH, but also to completely submerge the gearing to prevent corrosion. An IGH primarily needs a lubrication that's not going to evaporate and leave a sticky varnish behind, and to provide a measure of corrosion protection for the parts. RJ the bike guy recommends Phil Wood oil to rebuild a 3 speed, because it'll stay where you put it. To use the oil port, Sturmey archer recommended a 5W weight light machine oil, and just a drop weekly in regular use to help flush metal filings from the contact points, and lubricate the bearings.
Overlubrication will wash the grease (if you used grease) from the bearings, and provide a sticky protective film to the hub shell, and just about every everywhere the hub drips.