First, most lysogenic phages will form turbid plaques (and not clear ones).
Secondly you can isolate the lysogens from the center of those turbid plaques and show; 1) they are immune to the same phage so that the phage will not form plaques on the strain; and 2) it will release phage again (usually). An overnight culture from such a presumed lysogen can be centrifuged to remove the cells and then you will find phage in the supernatant that you can titer.
There are always some exceptions to these but in general these are the simplest way to experimentally determine.
If you want a molecular approach you could develop PCR primers to the phage and grow presumptive lysogen and show they carry the phage. But to do this properly you need to restreak a few times and to make sure you don't have any contaminating phage along for the ride that would also give you PCR product.
2. After incubating phage and bacteria the resultant culture mostly after 2 hrs will become so turbid like no phage added in the mixture,usually lytic phage containing culture takes time to get turbid.
Kinldy note down
Above properties sometimes can be shown by some lytic phages too, so correlate with WGS resltults accordingly .