What it is
Lanolin is a wax that sheep secrete from the sebaceous glands in their skin to keep their own fleece soft and water-repellent. It is recovered as a byproduct of the wool trade: freshly shorn wool is scoured in hot water and detergent, and the grease that washes out is lanolin, which makes up somewhere between 5 and 25 per cent of the weight of raw wool. A single merino sheep can yield a few hundred millilitres of it a year. Chemically it is about 97 per cent long-chain waxy esters, and despite old names like wool fat it holds no glycerides, so it is not a true fat at all. The point that matters for this question is that no sheep is killed to produce it, which is why some people wave it through; but it is still a substance taken from an animal's body for human use, and that is the line veganism draws.
Why it catches people out
The lanolin most shoppers never picture is the kind they swallow. The US Office of Dietary Supplements says vitamin D3, or cholecalciferol, is typically made by irradiating 7-dehydrocholesterol drawn from lanolin, itself taken from sheep's wool, so the ordinary D3 in supplements, fortified plant milks and breakfast cereals usually began life on a sheep's back. There is a true plant-based route, D3 made from lichen, and there is vitamin D2 made by irradiating a yeast sterol, but neither is the default, and a label reading only 'vitamin D3' or 'cholecalciferol' tells you nothing about which was used. On the outside of the body, lanolin turns up in moisturisers, lip balms, the nipple creams sold to new mothers and a great many ointments, valued for the way it keeps water against the skin. If avoiding it matters to you, the practical move is to choose a D3 that names lichen as its source, or a D2 supplement, and to treat a bare 'cholecalciferol' as a question rather than an answer.