LightInject | An ultra lightweight IoC container

In general, injecting an IServiceProvider (or any abstraction that gives access to an unbound set of dependencies is a bad idea, because it can lead to the Service Locator anti-pattern. A discussion on this anti-pattern can be found here.

A Service Locator is something that only exists outside the Composition Root. Your BackgroundService1, however, might be part of the Composition Root, which might injecting a DI Container -or an abstraction there over- a feasible solution. Note that you should strive keeping all business logic out of the Composition Root. This ensures that BackgroundService1 purely functions as a mechanical peace of code that delegates the operation to classes that run the actual business logic.

Though, when operating inside the Composition Root, there is typically no need to use an abstraction over your DI Container, such as an IServiceProvider. The Composition Root already has intrinsic knowledge over all application's dependencies, including your DI Container.

This means that you can inject LightInject's ServiceContainer directly into the constructor of BackgroundService1; there is no need for an IServiceProvider.

If, however, you insist in using the IServiceProvider abstraction, you can create an IServiceProvider implementation that wraps ServiceContainer and forwards its GetService method to the wrapped ServiceContainer. This wrapper class can than be registered in the ServiceContainer.