Sorry, LR is Lightroom and there is a filter effect tool, including orange. It does, generally, mimic the orange filter effect on the film by changing skin tones, etc... but I started to wonder if it was truly a replacement or not.
Your answer would be best served by asking in the "DPUG" forum, they are into digital image manipulation. In fact i think discussing such topics is almost forbidden here.
But if you want an answer, i don't know if you are comparing the effect applied on the scan of a color film, or the effect applied on a digital image created by a digital camera.
If the image was created by a digital camera, i think you already know that in such a camera the amount of red pixels is about 1/4th of the amount of total pixels. This means that applying a strong or red filter will dramatically reduce resolution and also increase noise (because noise on the red channel is usually higher). So it's not really a perfect solution.
As for the result, it may not necessarily be the same, because B&W film has a peculiar color response different to color film; in fact different B/W films can have different spectral response (i.e. FP4 versus Fomapan 100), and thus even without a filter, the result will be different to what it is achieved digitally.
And again, remember that you can't digitally apply an "orange filter effect" on a B/W digital image, because there is no color information there.