class QMyLineEdit : public QLineEdit
{
    Q_OBJECT
    Q_PROPERTY( QString action_icon READ GetIcon WRITE SetIcon )

public:
    explicit QMyLineEdit( QWidget* parent )
        : m_pAction( nullptr )
    {
        m_pAction = new QAction( this );
        connect( m_pAction, &QAction::triggered, this, &QMyLineEdit::MyAction );
        addAction( m_pAction, QLineEdit::TrailingPosition );
    }

private:
    QAction* m_pAction;
    QString  m_strIcon;

    const QString& GetIcon() const
    {
        return m_strClearIcon;
    }
    
    void SetIcon( const QString& strIcon )
    {
        m_strIcon = strIcon;
        QIcon Icon( m_strIcon );
        m_pAction->setIcon( Icon );
    }
    
    void MyAction(){ /* ... */ } 
};

// Stylesheet
.QMyLineEdit {
    qproperty-action_icon: url(:/Widgets/action.png);
}

.QMyLineEdit:read-only {
    background-color: green;
    qproperty-action_icon: url(:/Widgets/action_readonly.png);
}