Whenever you disqualify the lead it save the Lead form, so you can have JS registered on save event to check if user initiated action to disqualify lead
In this case you need to check for savemode() equal to 15 on save event of lead
execObj.getEventArgs().getSaveMode()
Entity Event Mode Value AllSave1AllSave and Close2AllSave and New59AllAutoSave70ActivitiesSave as Completed58AllDeactivate5AllReactivate6User or Team owned entitiesAssign47Email (E-mail)Send7LeadQualify16LeadDisqualify15
Source:
https://msdn.microsoft.com/en-us/library/gg509060(v=crm.6).aspx
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