Unity Cosmetics products contain no form of wool fat / lanolin whatsoever.
Wool fat or lanolin
Wool fat is also called lanolin alcohol (or lanolin). It's obtained from a sheep's fleece — sheep have sebaceous glands that secrete a yellowish sebum. You can easily see this sebum in a fleece: small yellow droplets. After shearing, the wool is washed and these droplets of sebum come away from the fleece. The water is then evaporated and a yellowish substance remains; it is called wool fat or lanolin. Structurally it's wax-like — a hard, solid fat. It's often added to cosmetics, especially skin products such as creams, because it absorbs easily into the skin and holds moisture. That makes it hydrating and soothing.
Although wool fat is often colloquially called lanolin, there is a small difference between the two terms. Wool fat consists entirely of the fat from a sheep's fleece, while lanolin is often a blend of wool fat and another ingredient (such as petroleum jelly).
A very small proportion of people with allergies are allergic to wool fat and therefore also to lanolin (because lanolin partly consists of wool fat). In most cases this involves wool fat that hasn't been purified. You'll recognise unpurified wool fat by its yellowish colour. Unpurified wool fat can seal the skin, which can clog pores. That can lead to inflammation. Once wool fat is purified, the colour is no longer yellowish but white. The structure of purified wool fat differs from unpurified wool fat, and purified wool fat doesn't seal the skin. Generally speaking, purified wool fat is well tolerated by the skin. Unfortunately, the ingredients list won't tell you whether the lanolin/wool fat present has been purified.
Both wool fat and lanolin are listed as "Lanolin" on the ingredients list. Because it's impossible to tell whether wool fat / lanolin has been purified (the only way is to ask the supplier/manufacturer), Unity Cosmetics doesn't use any wool fat / lanolin in its products at all.