Lysogenic cycle of viruses is characterized by integration of its nucleic acid into the host’s genome. The genetic virus is then transmitted to daughter cells at each subsequent cell division.
Lytic cycle is the life cycle of virus characterized by destruction of the infected host cell and its cell membrane.
When HIV first infects a person, it becomes dormant and harmless for months or even years in the host genome. There it belongs to lysogenic cycle. Once it starts to replicate (acute infection), HIV enters the lytic cycle cells and release large amounts of the virus.