Can you issue a warning for this?: Answer
Answer: No.
The National Labor Relations Act (NLRA) protects an employee’s right to discuss union organization during non-work times, such as breaks, and in non-work areas, such as lunchrooms and parking lots – even when they are on the employer’s premises.
Employers may not prohibit employees from discussing wages or even unionization. As a representative of the company, you may not interfere with an employee’s right to discuss unionization with other employees or with a third party, including a union organizer.
Disciplining the employee for this lunchtime activity would likely be viewed as an unfair labor practice, which could trigger a charge from the National Labor Relations Board (NLRB). An acceptable course of action would be to inform someone in management about any witnessed union activity. Management can then follow the appropriate NLRB guidelines for a counter campaign if they wish.