Lathe work should be finished to the fineness obtained with 320 grit paper. Steel wool may be used, or one of the specialists tools now available. A technique using small sanding discs mounted in an electric drill, and bearing on the work whilst rotating at low speed also gives very good results.
Chinese Wood Oil or Red Oil is applied using a rubber cupped under the wood while the lathe rotates at its lowest speed.
Oil is applied more liberally than when hand polishing to prevent the heat caused by friction from making the rubber snag into the wood.
It as a far quicker application of polish to the wood than by hand and bodying up for filling of the grain occurs very quickly. Wet and dry paper 1000 or 1600 grit also steel wool can be used with good effect on the lathe.
Again: KEEP THE SPEED LOW!