Nuclear envelope breakdown
All nuclear replicating viruses must get their progeny out of the nucleus. This process requires dedicated viral proteins. Indeed it is unnatural for a cell to let DNA or un-spliced RNA material escape from the nucleus.
Viral capsids can escape out of the nucleus by disrupting the nuclear membrane envelope. This process can take place before any cell lysis, and for some viruses virion assembly is completed in the cytoplasm.
The disruption of the nuclear envelope is an active process induced by specific late viral proteins. The exception is papillomaviridae viruses that infect epithelial cells and rely on passive lysis during host cell desquamation.