Well those drugs you listed are all Controlled substances (class 3-5), none of those are narcotics. Narcotics are generally class 2, although certain places will call those narcotics. Anyway, mainly controlled substances are kept in lock boxes because they are benzodiazepines, and if overdosed can be a hazard to health (or deadly). If you want to know what would be in that lock box, just look for a list of class 2-5 controlled substances (anything from oxycodone, adderal, morphine, fentanyl to gabapentin, valium, diazepam) However the unit may or may not keep narcotic pain killers on the floor, but the class 2's you listed make sense as they are often used to reduce CNS synapse and promote sedation or relaxation.
In addition it may be the facility policy, however its common for controlled substances to be counted. if those medications go missing the DEA comes down pretty hard. as for the IM ativan, id ask the unit manager but if i was to guess it would be because it may be used in emergencies or its not a high risk because of the injection being neccessary and lack of access to the fridge (if its in the back of the facility)