This model of reality (the medieval idea that the world is a battleground between good and evil)
lived on, (continued to exist in later ages)
Overlaid by different conventions (altered or evolved by other, new ideas)
In the more sophisticated Elizabethan works of the following age (in the plays and books written during the more complex Elizabethan age that followed.)
In your example text, the Medieval mental model of the world as a battlefield between good and evil is portrayed by the Morality plays of that period. That concept or model of the world, in the later Elizabethan period, became the underlying or central structure of a new mental model that took that idea and added new ideas and overlaid them (layered over the top), in the same way that muscles overlay a skeleton, or paint overlays (is painted on) a building. This new Elizabethan model of reality (as portrayed by the works of that time) had its origin or roots in the original Morality play model of reality, but was a altered or refined version of that original concept.