Can lysozyme also lyse gram-negative bacteria and if yes, how fast?
Gram-negative bacteria also have peptidoglycan which can be degraded by lysozyme. However they have an outer membrane lying outside the peptidoglycan layer and this will block lysozyme action. 

Because of this if you intend to treat Gram-negative bacteria with lysozyme it is necessary to add something that will disrupt the outer membrane—the usual choice is EDTA since removal of magnesium ions by chelation will destabilise the outer membrane.