As you want to achive parallel processing, using a Task and async processing would be a good approach.
Therefore, you need to define a method or expression that will be your Task/Action and includes a retry pattern internally:
public const int MAX_RETRY_COUNT = 3;
private void ProcessItemsAsync(Item item, int retryCount)
{        
    // Note: Exceptions thrown here will pop up
    // as AggregateException in Task.WaitAll()
    if (retryCount >= MAX_RETRY_COUNT)
        throw new InvalidOperationException(
            "The maximum amount of retries has been exceeded");
    retryCount++;
    // Either implement try-catch, or use conditional operator.
    try
    {
        // Do stuff with item
    }
    catch(Exception ex)
    {
        // Exception logging relevant? If not, just retry
        ProcessItemsAsync(item, retryCount);
    }
}
Once you defined your Task method, you can process a bulk of tasks at once:
public const int BULK_AMOUNT = 10;
private async void ProcessSqlData()
{
    List<Item> lstItems = await UnitOfWork.Items.GetAllAsync();
    for (var i = 0; i < lstItems.Count; i += BULK_AMOUNT)
    {
        // Running the process parallel with to many items
        // might slow down the whole process, so just take a bulk
        var bulk = lstItems.Skip(i).Take(BULK_AMOUNT).ToArray();
        var tasks = new Task[bulk.Length];
        for (var j = 0; j <= bulk.Length; j++)
        {
            // Create and start tasks, use ProcessItemsAsync as Action
            tasks[j] = Task.Factory.StartNew(() => ProcessItemsAsync(bulk[j], 0));
        }
        // Wait for the bulk to complete
        try
        {
            Task.WaitAll(tasks);
        }
        catch (AggregateException e)
        {
            Log.WriteLine(String.Format(
                "The maximum amount of retries has been exceeded in bulk #{0}. Error message: {1}",
                i,
                e.InnerException != null
                    ? e.InnerException.Message
                    : e.Message));
        }
    }
}
However, if you know that your computer running this has enough performance, you might increase the BULK_AMOUNT. You should test it, to find the optimal amount here.