Depending on the context, "class" can mean several things. In reference to a show or exhibition, class describes a specific age group of animals, for example, spring yearling heifers. When discussing livestock in general a class refers to the age or stage of production. For instance, calves are typically animals that are less than 1 year old; feeders are cattle that weigh less than 700 pounds and have not entered the feed yard for finishing. Heifers are female cattle that have not given birth to a calf yet.
A "project" can refer to a specific learning activity. With regards to livestock, this could be a market beef project, a breeding heifer project or a market lamb project. It would involve rearing the animal from weaning or purchase through harvest.
A "lot" refers to an individual animal or set of animals in a consignment sale, or as an entry in a show or expo.
The lot is the type of project/class that you are doing, it is more refined in definition. Example: Beef is a class. Spring heifer calf is a lot.