An emulsifier creates some thickness, but sometimes not enough. Once the correct amount of emulsifier has been added to properly emulsify the oil and water, it is better to add some type of thickener to get the desired viscosity, rather than add more emulsifier. The functions of a thickener like stearic acid are to add additional thickness to the product and to help stabilize the emulsion over the normal range of temperatures the lotion will see.
You are right that butters (mango, shea, etc) if present also act as thickeners, but be aware of their limitations. They might work fine in winter, but some butters soften and melt at normal summer temperatures, which can cause your lotion to become too thin. A thickener like stearic is stable at normal ambient temperatures.
If you think your butters and/or your emulsifier may thicken your recipe well enough without a separate thickener, leave it out and see how your lotion works. Nothing horrible will happen if you do. If the emulsion is not as long-term stable as you would like or the lotion is too fluid for your preference, then add a touch of thickener back in.
Another thickener you may want to look into is cetyl alcohol. Cetyl has a lighter skin feel a little more like whipped cream. Stearic creates a heavier skin feel, a bit like sour cream.
Your choice of emulsifier will also affect skin feel. E-wax (emulsifying wax) is an all-in-one emulsifier that works well for home crafters. It tends to give a "glidy", greasier feeling to a lotion. Conditioning emulsifier (BTMS is one company's product for this type of emulsifier) is another all-in-one emulsifier that gives a drier, more powdery feeling to a lotion.
(A side note: Conditioning emulsifier is also nice for a hair conditioner because it can "stick" to the hair shaft due to it's electrical charge. A product made with e-wax will not condition hair because e-wax has no electrical charge -- it can't stick to the hair and will just rinse right off. You can even make a super simple, basic hair conditioner just with conditioning emulsifier, water, and preservative.)
With all that said about thickeners and emulsifiers, I am also wondering about your choice of fats and the percentage of water in your lotion. These factors also play a big role in skin feel. To make a drier, lighter lotion, omit or reduce the butters. Of the butters you might use, substitute drier butters (mango, babassu, illipe) in place of greasier butters (shea). Minimize or eliminate heavy oils (olive, avocado, almond, rice bran, sesame, castor, etc) that absorb slowly and have a waxy or greasy skin feel. Switch to lighter, drier oils (jojoba, fractionated coconut, meadowfoam seed, camellia, hemp, apricot, etc.) that absorb quickly and have a silky skin feel.
Play with increasing the water content for a lighter lotion that might feel nicer in warm weather. A lotion with 70% water is fairly heavy which is great for winter. Increase the water to 80% in the same recipe and the skin feel changes dramatically. A lighter lotion will mean you will apply less oil to your skin and that may reduce the sticky, oily feeling you don't like. If you are using an ineffective emulsifier, the more watery the lotion, the more likely your emulsion will separate and fail.
I'm going to add a gentle plug for preservatives, in case anyone reading this has not been using a reliable preservative in oil-and-water lotions. Fungi and bacteria are very natural organisms, and they thrive in "all natural" oil-and-water emulsions made without preservatives. A fungal or bacterial infection of the skin or eyes from a contaminated lotion can be serious and life changing. Making a lotion without a preservative is similar to not wearing eye protection when making soap. It might be fine most of the time, but one tiny lye splash in the eye can have life changing, permanent consequences. It's so not worth the risk!