I've been doing what machinists have been doing forever- using a pump oil can or brush in a can of cutting oil. For cutting oils:
-Dark Sulfur cutting oil, available at Home Depot and Lowe's (usually in the plumbing department as it used for threading pipe) works quite well for drilling and turning of most carbon steels. It is inexpensive. The downside is it makes a mess of the machine and does smell somewhat.
-Light Cutting Oil, also offered to plumbers, is a pretty good alternative.
-for turning or machining aluminum: spray on WD-40. Aluminum must have a thin lubricating cutting fluid. Oldtimers used straight kerosene. for a small lathe, WD-40 in a pump container (buy a gallon and get a hand squirt container) will be plenty good.
-Lard Oil: This is the oldest and one of the best cutting lubricants. It has been used by machinists since the beginnings of the art. Oldtimers simply took the bacon drippings from the skillet or griddle, and used them as cutting lubricant. I mix my bacon drippings about 50:50 with diesel fuel and then add a little "tractor hydraulic fluid" (which is DTE Heavy Medium, a good all purpose oil for plain bearings or other mechanism parts). I pour off the bacon drippings while they are HOT and fluid, getting them into a good sized can. Once I have the drippings in the can, I head out to the garage and pour in the diesel fuel and tractor hydraulic fluid. Mixing while the drippings are fluid and hot assures a uniform cutting oil with no globs of lard floating around. This works wonders when turning steels, stainless steels, as well as for milling, drilling, reaming and tapping. I put it on with an old pump oil can. It is far less messy and nowhere near as aromatic as Dark Sulphur Cutting Oil.
IMO, a 9" Southbend lathe is not a machine that will need a coolant system. Unless a person were running heavy long cuts or running production work, I would not think a recirculating coolant system is required.
We do use the portable misting systems on the machine tools in the powerplant shop. This system uses compressed air to aspirate and atomize a fairly concentrated coolant. The coolant is formulated for this type of misting device. When we machine austenitic stainless steels or drill stainless steels, we have found the misting system makes a world of difference. However, the misting system is total loss and creates an airborne mist that gets all over the machine tools and into the ambient air. for a home shop in a small space, this misting system would not be a real good idea.
I keep an old kippered herring tin on the lathe with a brush for putting on the cutting oil, and I keep the pump can full of lard oil/diesel fuel mix in close reach. I also keep a spray can of any cheap penetrating oil for machining aluminum. The word is WD 40 works the best, but I use what is at hand and make out OK.
Another thought: if the 9" lathe does not have a chip pan, you might want to make one and get it between the lathe and the bench or stand. A chip pan makes a world of difference in how clean the rest of the shop stays. Cutting oil soaking into a wood bench top, or simp
BTW: re: dark sulfur cutting oil. The stuff has been around forever and it does work. As a little kid, I remember my father always had a can of "Hercules" Dark Sulfur cutting oil in our home shop. We lived in one apartment of a 4 family house my Dad owned. The piping was vintage 1920's, screwed red brass and screwed galvanized for the water, screwed black iron for the gas and steam heat. Sooner or later, either the hot water ate out a valve, or something needed dismantling such as re-pitching the radiators to get rid of condensate knock. We usually wound up cutting and threading and "letting in a union", so the dark sulfur oil got plenty of use. Dad kept the dark sulfur oil in a "Goldenrod" pump oil can. As a little guy, I'd squirt the oil while Dad heaved on the diestock. Dad swore if he did not get the dark sulphur oil on the threading, the die chasers would tear the threads.
One day, when I was about 8, I was wearing a pair of Sears Roebuck coveralls my mom cut down and took in to fit me. I was helping my Dad with some repair or other on a Saturday. Dad asked me to go to the corner mailbox and drop some letters. As I started down the street, the older kids started ragging me about the coveralls and my walk (which has a kind of bounce to it). The block bully, a kid of 16, a real nasty lug who was well over 6 ft tall, got behind me and started spitting phlegm onto my head. Of course, the crowd of other toadies egged him on. I knew if I tried anything, I was going get rat packed and smeared onto the sidewalk. I held my peace and vowed revenge.
Come the next weekend, pretty much the same scenario. Dad asked me to go to the corner mailbox. I detoured to the pipe vise and put the Goldenrod oiler full of Hercules Dark Sulphur Cutting oil in my pocket along with a rag. I proceeded down the street, taking my time. The loafers on the stoop of this one house were in full cry about my walk, my coveralls, and all else, asking if I wanted anymore spit on my head. Out came the block bully, and he got behind me. I heard him rasping and working up to fire a round onto my head. It was every bit as juicy a victory as david and Goliath. I turned around and nailed him full in the eyes with Hercules Dark Sulfur Cutting Oil before he ever had a chance to let fly with his lunger. I kept pumping, covering his head and clothing until the can was empty. The bully could not move, screaming and howling. The crowd switched sides in part, some hollering how I had "killed" the block bully (amazing how fast people can switch sides) , and some loyal toadies telling me I was dead. I was past caring, hoping there were some cuttings from the pipe reamer or diestock in the cutting oil, and imagining what an 18" Rigid wrench would do next time around.
Now for the funny part: The block bully was the son of an equally obnoxious and short tempered man who happened to be a licensed plumber. The licensed plumber had beat up at least one neighbor, and he had it in for my old man, who was a construction inspector. I told the old man what went down. He drew on his pipe and laughed, touseled my hair and said: "Let the s--b's come on, they can all go to hell." I never had another problem and never heard another crack about my coveralls or my walk from the whole sorry bunch.
The plumber must've known what his son had been up to, or maybe he was afraid to tangle with my old man, as we never heard another word out of them.
Dark sulphur cutting oil- GREAT STUFF !!! who needs "conflict resolution" or whatever the new "politically correct" solution to disputes is ? Dark Sulphur Cutting Oil, works like a champ and leaves 'em rolling on the sidewalk, not knowing what hit 'em.