Andy, 

The expression is ‘ servir qqc à qqn ‘ with both a direct and indirect object.

Whatever it is that ‘que’ represents in this sentence is the direct object of ‘servir’ and the agreement is with that direct object. There is also the indirect object ‘ lui ‘ which doesn’t affect agreement.

Without having listened to the exercise, I am assuming from the title the direct object may be ‘ l’omelette ‘, but whatever it is, as long as it is grammatically singular feminine, there is no error or typo. Here is another example ‘ La viande qu’il m’avait servie … ‘.

 Que = Whom/which/that (French Relative Pronouns) 

https://www.wordreference.com/fren/servir

 Special cases when the past participle agrees (in number & gender) when used with 'avoir' in the compound past in French (Le Passé Composé)

Bonjour Andy,

I can't see a case for it being written as servie.

The verb servir only takes avoir as auxiliary and l'aubergiste is male or female.

The subject of the clause after que is l'aubergiste and servir is transitive indirect with lui.

So I am inclined to agree with you.

Bonne journée

Jim