Plaster and stucco must be attached to a base layer that supports the cementitous material structurally. This is typically a type of lath, in the past this was often strips of wood attached to the wooden studs of the wall. Over the wooden strips a mixture of lime, sand, cement and horse hair was often used. That is where the term horsehair plaster comes from. This was the method of building most common until around the 1930s. At that time, Portland Cement began to enter the US market and the building methods slowly evolved.
During World War II metal lath had not yet become popular and a burlap solution was a choice solution as a plaster base. The burlap would be hung from a ceiling and attached to the floor, a soupy stucco mix would be applied as a base coat basically to saturate and then stiffen the burlap. This was a method for building interior walls. Two plasterers would work in unison opposite each other to apply the first layer, it would dry for 3 days and once it was set up and stiff one side would receive a second layer. After two days of drying the other side would receive its second layer. Two days after that a third layer would be applied to each side. After installing any doors or windows into the framed designated areas, additional stucco would be applied up to the level of the wood studs.
Today there the most common lath used is expanded metal sheets, welded wire lath or even chicken wire. There are also plastic and fiberglass options that have a number of benefits over metal, one example is a product called SpiderLath.
When applying a stucco or plaster over a concrete block or a cement wall, lath is only needed if that wall has a layer of paint or waterproofing material over it. Or, if it will not allow a fresh layer of cementitous mix to adhere to it. The easy way to explain this is a phrase such as “Like to Like.” This refers to cementitous surfaces or brick or stone walls that are clean and can accept a layer of stucco or plaster. Other names for a concrete block wall include cinder block and CMU or concrete masonry units. One way to test if a wall has a waterproofing layer over it is to spray a light coating of water onto it, if the water absorbs into the wall quickly then it most likely has not been coated, if droplets form on the surface that means it likely has a sealer over it and will need a layer of lath before applying any stucco or plaster.
If the surface receiving the stucco or plaster is wood, metal or a coated brick, block, stone or concrete wall it will require a layer of lath to allow the stucco or plaster to properly adhere to it.
More details on this subject are available in The Stucco Book, The Basics by Herb Nordmeyer