This article about Working with HttpContext.Current might help. The key, for you, might be that when control passes from one thread to another HttpContext.Current in the new thread can be null.
Here is another question/answer from here on SO that describes HttpContext.Current being null in the context of a web service. The accepted answer suggests turning on ASP.Net compatibility in your web.config file.
I don't know of either of these will help, but they might. I found them by googling for "HttpContext.Current is null", which yielded quite a number of hits. I have done very little ASP.NET development, so I can't really comment on HttpContext.Current from my own personal experience.
Given your use case, I would suggest that you look into System.Diagnostics.CorrelationManager.ActivityId.
One nice feature of ActivityId is that it is "flowed" from parent threads to child threads (including thread pool threads). I think that it works well with Tasks and Parallel operations. Works well meaning that the ActivityId, as set in a parent thread, has the expected value in a child thread.
There is not a LayoutRenderer for ActivityId, but it easy enough to write one. See an example (written against NLog 1.0) here:
Most useful NLog configurations
I'm pretty sure that the "EstimatedBufferSize" stuff is no longer needed, so something like will probably work:
[LayoutRenderer("ActivityId")]
class ActivityIdLayoutRenderer : LayoutRenderer
{
protected override void Append(StringBuilder builder, LogEventInfo logEvent)
{
builder.Append(Trace.CorrelationManager.ActivityId);
}
}
If you go this route, you might consider adding a Format property to the ActivityIdLayoutRenderer to allow you to specify the guid format. See this answer (from me). It contains a lot of useful information about working with guids.
NewGuid vs System.Guid.NewGuid().ToString("D");
See this source file (in NLog's git repository) for an example of how you can implement and use such a Format property:
https://github.com/NLog/NLog/blob/master/src/NLog/LayoutRenderers/GuidLayoutRenderer.cs