var query =  
        from mvmt in applicationDbContext.Movements
        join mvmteq in applicationDbContext.MovementEquips on mvmt.MvmtId  
        equals mvmteq.MvmtId
        join equip  in applicationDbContext.Equipment on mvmteq.EquipId equals 
        equip.EquipId into g
        from mvmteq in g.DefaultIfEmpty()
        where mvmt.MvmtId != null
        select new
        {     
          MvmtId = mvmt.MvmtId,
          MvmtDescr = mvmt.MvmtDescr
         }).ToList();

请参阅https://learn.microsoft.com/en-gb/dotnet/csharp/linq/perform-left-outer-joins
和
http://msdn.microsoft.com/en-us/library/bb397895.aspx

Movements = (
            from mvmt in applicationDbContext.Movements
            join mvmteq in applicationDbContext.MovementEquips on mvmt.MvmtId equals mvmteq.MvmtId into join_1
            from mvmteq in join_1.DefaultIfEmpty()
            join equip in applicationDbContext.Equipment on mvmteq.EquipId equals equip.EquipId into join_2
            from equip in join_2.DefaultIfEmpty()
            select new GetMovementRequest
            {
                MvmtId = mvmt.MvmtId,
                MvmtDescr = mvmt.MvmtDescr,
                MvmtMetrics = mvmt.MvmtMetrics,
                MvmtStandard = mvmt.MvmtStandard,
                EquipId = equip.EquipId,
                EquipDescr = equip.EquipDescr
            }
        ).ToList();

• 您确实不需要OUTER JOIN查询。
• 如果要加载所有Movement和所有Equipment数据，则需要执行以下操作：

static async Task<( IReadOnlyList<Movement> allMovements, IReadOnlyList<Equipment> allEquipment )> LoadEverythingAsync( this ApplicationDbContext db, CancellationToken cancellationToken )
{
    IReadOnlyList<Movement>  allMovements;
    IReadOnlyList<Equipment> allEquipment;
    {
        List<Movement>  mov = await db.Movements.ToListAsync( cancellationToken ).ConfigureAwait(false);
        List<Equipment> eqp = await db.Equipment.ToListAsync( cancellationToken ).ConfigureAwait(false);

        await db.MovementEquips.LoadAsync( cancellationToken ).ConfigureAwait(false);

        allMovements = mov;
        allEquipment = eqp;
    }

    return ( allMovements, allEquipment );
}

上面的代码“工作”是因为实体框架DbContext执行 * 魔术 * 每当您加载数据到DbContext（从ToListAsync和LoadAsync），使所有附加和加载的实体将有他们的引用和导航属性的setter调用。