Does Tobacco mosaic virus replicate through the lytic or lysogenic cycle?

Well TMV definitely does not lyse cells, but it also doesn't integrate into the host genome and replicate. What it does is that it enters the host cell and has the host cell translate and transcribe it's viral RNA. This results in viral proteins, and new TMV "babies" are created. However, the host cell doesn't just burst. Instead, the new TMV's "bud off" of the host cell. TMV slowly works the host cell to death, making it create new TMV's to infect more host cells.