The GMB won a legal ruling over its bid to negotiate for more than 200 warehouse workers at the site but the firm is challenging the decision.
Supporters protested outside a Lidl store in Cardiff, saying further demonstrations will be held.
The company has argued that staff are already "fairly represented" in the business without unions.
GMB regional secretary John Phillips said: "Lidl must abandon attempts to subvert these rights and begin to bargain with their employees and to extend collective bargaining to their hard pressed retail workers.
"Promoting value for consumers must not be at the expense of workers' rights and decent labour standards."
In August, the Central Arbitration Committee (CAC), the independent tribunal with statutory powers over trade union recognition, dismissed Lidl's attempts to block warehouse workers in Bridgend from having union representation.
But the German-owned supermarket chain described that decision as "disappointing" and continues to challenge it.
"We continue to believe that our employees are fairly represented within the business, without having to deal with trade unions and creating a divided workforce," said a spokesperson following last month's ruling.
The firm has 637 stores and nine distribution centres in Britain, employing about 18,000 staff.
Trade union members have held a rally in a dispute over recognition at a Lidl supermarket warehouse in Bridgend.