[SalesForce] How create task for lead object through process builder

I do not see where you are checking for record type is your trigger so going to add that in the answer. As per others commented you need to set the whatID for the Owner.

Another issue you need to account for is assignment rules. If the owner changes then you may want to reassign the tasks to the new lead owner. You would query for the tasks related to the leads where the owner is changing and update the task owner appropriatly

trigger CreateTaskOnLead on Lead (after insert) {
    Map<ID,schema.RecordTypeInfo> lead_RT = lead.sObjectType.getDescribe().getRecordTypeInfosByID();

    List<Task> lTask = new List<Task>();

      if(Trigger.isAfter && trigger.isInsert) {
           for(Lead l: Trigger.new) {

               if(l.LeadSource == 'Property'){
                 if(lead_rt.get(l.RecordTypeID).getName() != 'Registration') continue;
                 task t = new Task( 
                 whatID = l.id,
                 Subject = 'Property',
                 Priority = 'Normal',
                 Status = 'Not Started',
                 Type = 'Action',
                 ownerID - l.ownerID
                 );
                 lTask.add(t);   
               }
            }
        insert t;
      }
}

As Eric has suggested to create a multiple steps and then you can use a third option "Customize Logic"

Check Customize the Condition Logic in Process Builder as a reference