That is a tough one. Woods that have high oil content like teak, ebony, and bloodwood are notorious for causing this problem when sanding. A few approached that might help.
Apply a spray sealer before sanding. Shellac is good because it does not react with the oil in the wood. Don’t use a brush since it will spread the oil. The sealer will block the pores of the wood and help keep the unwanted dust out. Lightly sand and if needed apply more sealer.
Use compressed air. While sanding on the lathe, use compressed air to blow the dust away quickly before it embeds in the wood.
Keep your sandpaper clean
Try shear scraping to get a good enough finish of the tool so sanding is not needed