Water + Oil + Sodium Hydroxide = Soap
Water + Oil + Emulsifier = Lotion
That's if all goes well, and there's obviously more to both of them than that. When I learned about lotions a few years ago, I heard about emulsifying wax (sometimes called E-Wax). It's a popular emulsifier for homemade lotions and it works well. Melting the wax and blending it in while still hot to your oils and waters creates your lotion.
A bit later I read about BTMS 50 (INCI: Behentrimonium Methosulfate (and) Cetearyl Alcohol), a conditioning emulsifier. It works well in conditioners, and when used it lotions it can give a powdery feel to the skin. This is a cationic emulsifier, so some preservatives might not work with it.
Some makers use beeswax and borax to create a natural emulsifier, but it doesn't create a stable emulsion. These will need to be shaken to mix the water and oils back together. I find separated lotions kind of gross, and usually toss any I have once they do separate. These lotions were using different emulsifiers and took a couple of years to separate. I'd be disappointed if I had one breaking down so soon.
In my recent experiments I am trying Olivem 1000 (INCI: Cetearyl Olivate (and) Sorbitan Olivate). An olive derived emulsifier sounded cool, plus it emulsifies by forming liquid crystals. But it does have some issues with stability. Adding a thickener like xanthan gum or a co-emulsifier helps stabilize it.
There are a lot of other emulsifiers out there, but these are the three I've tried. I haven't tried (or been tempted to try) the beeswax and borax method.
I'm not particularly interested in emulsifiers, but here are a few things you might want to look into if you are:
Use of silicones
Types of emulsion: Water in Oil, Oil in Water, Water in Silicone
Self-emulsifiers (you don't need to add additional oils to some of these)
Type of product (lotion, conditioner, spray, etc.)