Continuation indents should be 8 spaces. So this is going to look weird either way. It would look better by introducing a variable for the module:

        Module module = (Module) new Module()
        {
            @Override
            public void configure(Binder binder)
            {
                LifecycledBindingBuilder.lifecycleBinding(binder, Foo.class).toProvider(provider);
            }
        };
        Injector inj = new Bootstrap(module)
                .doNotInitializeLogging()
                .strictConfig()
                .initialize();