using System;

using System.Collections.Generic;

using System.Linq;

public class Program

{

    public static void Main()

    {

        var list = new List<Category>{new Category{Id=1, Translations=new[]{new Translation{Locale="EN",Name="aaa"}, new Translation{Locale="RU",Name="zzz"}}},

        new Category{Id=2, Translations=new[]{new Translation{Locale="EN",Name="ccc"}, new Translation{Locale="RU",Name="eee"}}},

        new Category{Id=3, Translations=new[]{new Translation{Locale="EN",Name="bbb"}, new Translation{Locale="RU",Name="aaa"}}}};

        var sortByKey = "EN";

        var orderedList = list.OrderBy(x=>x,new CategoryComparer(sortByKey));

        foreach(var item in orderedList)

        {

            Console.WriteLine($"ID={item.Id}");

        }

    }

}

​

public class Category

{

   public long Id { get; set; }

   public Translation[] Translations { get; set; }

}

public  class Translation

{

   public string Locale { get; set; }

   public string Name { get; set; }

}

​

public class CategoryComparer : IComparer<Category>

{

    private string _locale;

    public CategoryComparer(string locale)

    {

        _locale = locale;

    }

    public int Compare(Category x, Category y)

    {

        var orderedX = x.Translations.Where(c=>c.Locale.Equals(_locale)).OrderBy(c=>c.Name);

        var orderedY = y.Translations.Where(c=>c.Locale.Equals(_locale)).OrderBy(c=>c.Name);

        return orderedX.First().Name.CompareTo(orderedY.First().Name);

    }

}