Which structure is a network of membranous tubules in a eukaryotic cell and is continuous with the nuclear membrane?

The endoplasmic reticulum is indeed a network of membranous tubules that plays a crucial role in the synthesis and processing of proteins and lipids within eukaryotic cells. It is contiguous with the nuclear membrane, meaning that it directly connects to the outer membrane of the nucleus. This structural relationship enables efficient communication and transport of materials between the nucleus and the endoplasmic reticulum, facilitating the production of secretory proteins and membrane components that are translated from mRNA in the ribosomes associated with the endoplasmic reticulum.

The Golgi apparatus, while also involved in processing and packaging proteins, is not continuous with the nuclear membrane; it operates as a separate organelle that receives proteins from the endoplasmic reticulum. Mitochondria are involved in energy production through cellular respiration, and lysosomes function in the degradation and recycling of cellular waste, neither of which have a structural connection to the nuclear membrane. Therefore, the defining characteristics of the endoplasmic reticulum establish it as the correct answer in this context.