Here in Southern California, I don't have to contend with rust as heavy as that. Not close. Still, I use Boeshield T-9, SC Johnson Paste Wax, Renaissance Wax, and WD-40 to protect my iron and steel tools from rusting.
To clean up rust, including restoring neglected rusty tools that I have received from others, I use WD-40 and gray Scotchbrite pads. For severe rust problems, I use the green Scotchbrite pads, which are more abrasive than the gray. Mineral spirits is useful for cleaning and for removing wax. Use solvents and sprays in a well-ventilated area (I prefer outdoors). Wear protective gloves and an appropriate protective mask for the solvents and metal dust.
Boeshield T-9 is a combination of WD-40, paraffin wax, and mineral spirits. It is a good protective product. The paraffin wax does not glide as well as I'd like for the table saw or lathe ways, so I finish with SC Johnson Paste Wax. I reapply the paste wax periodically to keep surfaces protected and gliding smoothly.
SC Johnson Paste wax is inexpensive. A can will last a long time, and it costs $7 at Home Depot. The wax is easy to apply and buff out. No silicone. Many uses. Great stuff!
Renaissance Wax is used by museums to protect valuable ancient artifacts. It is expensive, but a small can will last a long time. It is a hard, durable synthetic microcrystalline wax. I use it on my hand tools (e.g., chisels) and measuring tools (e.g., Starrett combination square). It works great on my table saw, but is harder to buff out than low cost SC Johnson Paste Wax, so I use the SC Johnson Paste Wax on the table saw.
WD-40 is a petroleum solvent intended as a protectant, not really as a lubricant. The "WD" stands for "water displacement" - it is designed to penetrate and keep parts from rusting. The exact formula is a secret, like the formula for Coca-Cola or the 11 secret herbs and spices that the Colonel uses. I spray it on rusty surfaces and use it with Scotchbrite abrasive pads to remove rust. Others spray it and leave it as a protectant.
3M Scotchbrite pads are woven nylon "scrubbie" pads with embedded aluminum oxide abrasive particles. The ones I use are Gray, which is a mild abrasive. (Gray pads are also useful as an improved replacement for 0000 steel wool for wood finishing.) For very rusted tools, I may use Green pads sparingly. The green pads are much more abrasive. With any abrasive pad, use a sanding block for even pressure - you want to keep your table saw tables and lathe beds flat! You can find them in the paint section at big box stores. There are third-party brands also available and they tend to follow the same color scheme as 3M, but
In desperation for badly rusty tools, I have used Boeshield Rust Free, an acidic rust removal product. It works, but it is messy. Any overspray and splatters will remove paint, stain other nearby tools, etc. A few drops got on the aluminum beds for my spouse's small belt/disc sander. The spots turned black and I could not remove them.
Boeshield Rust Free came in a three-pack that I had bought at Rockler, but you can also buy it separately:
https://www.rockler.com/boeshield-3-part-tool-care-kits-and-lubricant
https://www.rockler.com/boeshield-rust-free-rust-and-stain-remover-8-oz-spray-bottle
I have heard of other people using other acids and other products for rust removal, including ordinary household vinegar. As I said above, don't let the acid splatter or splash on anything else, or it will remove paint and discolor metals permanently. Whatever you do, neutralize the acid as soon as you are done with it. I use water to dilute, wipe dry, and quickly follow it with WD-40.
Bottom Line: If I had your lathe issues, I would start with WD-40 and gray Scotchbrite pads. Use a sanding block to keep even pressure. If that doesn't work, then I would progress beyond that as described above.