The attached two pictures show my GMT 1HP 120VAC air cooled spindle. In one picture you can see a M5 threaded hole in the center of the spindle's body. The vendor said that it is for a set screw and to use a bolt to plug it.

I don’t believe this hole is for a set screw, I think it is for a grease nipple but the vendor said that the bearings are lubricated for life. The GMT web site has no info regarding this spindle

Anyone has an idea what this hole is for?

A high speed spindle like that would NEVER have a grease Zerk on it.  The bearings would be very lightly lubricated, and shielded to keep the grease in.  Grease it, and you'll ruin it.

Regards,
Ray L.