Aluminum tends to adhere to a cutting tool edge; this is called a Built Up Edge, or BUE. It is unclear if the aluminum welds to the cutter but however it forms it adheres very tightly, thereby ruining any cutting action. This applies to lathe tools and milling cutters. Coolants and cutting fluids prevent and/or reduce the formation of a BUE. WD-40 does this very well when cutting aluminum. It also alters the chip form, although this is most readily seen with carbide tooling.
You will find that a BUE will most readily form on carbide tools. It is less of an issue with a properly ground HSS tool ground for aluminum.
As far as I know, oil - any oil - is immiscible in water so no, it doesn't work as a coolant but some forms of oil can be used as a cutting oil or aid. Crisco comes to mind.
As for cast iron, yes, it is cut dry. Oil will form an extremely abrasive slurry that will wear your tool and your lathe very quickly. A dry cut allows the chips to clear from the cut, thereby reducing wear.
There are many cutting oils/coolants and you will learn to use different ones for different materials. WD-40 works well for aluminum but the aluminum-specific fluids are better; Relton A-9 for one. Specific operations may also influence your choices. For example, a sulfur-based cutting oil produces better results when threading or knurling, which produce extreme pressures at the tool interface.
Just as important as coolants or cutting oils is your choice of tooling. Mini-lathes in general are not rigid or fast enough to use carbide tooling to full advantage. HSS tools will, in general, work better on these smaller lathes. A properly ground tool will allow a little lathe to cut like a much bigger one so look into tool grinding. One popular option (I have not used them) for many hobby guys are the tangential tool holders that allow a novice to quickly grind and use HSS tools at low cost. I think if I was a new hobby guy with a mini-lathe, I would use one of these tangential tools until I could learn to grind a conventional HSS lathe tool. You can also used honed brazed carbide tooling but they will cut with higher cutting forces. I would avoid carbide insert tooling if I were you; your lathe is just not rigid enough or fast enough to use it.
Lots to learn and think about but give it time and it will come.