Are there differences in how adenoviral and lentiviral particles are produced?
Yes, there are. Adenovirus is a lytic virus, building up viral particles inside the host cell. Lysing the cells will release these viral particles.
Lentiviruses and retroviruses in general form particles at the surface of the cell and bud through the cell membrane, taking some of the membrane's lipid bilayer with it and encompassing the viral particle. The process of budding through the membrane is required for retroviruses and lentiviruses and therefore, titer will not be increased by lysing the cells.