C# - Locking An Application Variable?

I'm using a 3rd party web service in my ASP.NET application. Calls to the 3rd party web service have to be synchronized, but ASP.NET is obviously multi-threaded and multiple page requests could be made that result in simultaneous calls to the 3rd party web service. Calls to the web service are encapsulated in a custom object. My thought is to store the object in an application variable and use the C# lock keyword to force synchronized use of it.

I'm nervous, because I'm new to multi threaded concepts and I've read that you shouldn't lock a public object (which my application variable effectively is). I've also read that if the locked block of code fails (which it could if the web service fails), then it could destabilize the app domain and bring down the application.I should mention that the 3rd party web service is rarely used in my website and it's going to be rare that 2 requests to it are made at the same time.Here's a rough code sample of how I'd make calls to the web service:

ThirdPartWebService objWebService = Application["ThirdPartWebService"] As ThirdPartWebService;
lock (objWebService)
{
objWebService.CallThatNeedsToBeSynchronized();
}