Get field label in lightning component

You need to call server side controller from lightning and use following code (Describe API) there:

Schema.SObjectField F = fieldNameMap.get(fieldAPIName); //where fieldAPIName is API name of field
Schema.DescribeFieldResult R = F.getDescribe();
String fieldLabel=R.getLabel();
return fieldLabel;

This is the only way as far as I know. Else, you can create new custom labels for field names labels and use them directly in lightning using "$Label.c.Custom_Label"

Answer is:

This cannot be done in lightning component as of today!!!

please vote this idea to make this feature available sooner:

Access sObject field labels from lightning component