That's the one. It's different from the single that came with the BDB. The LM basket has a cylinder-ish-shaped mini chamber in the center that takes up to 7-9g.
The key is to only fill up the mini chamber in the middle and thus the need for a 41mm tamper for tamping. I had used that LM single basket with a BDB, it did work, but the puck was not 100% dry (the normal double basket aren't exactly dry either, but the single will be wetter). Most people wouldn't bother with a single for these reasons. If you're hell bent on getting singles right, I reckon they are the one to go for.
The LM single basket has been my daily go-to for more than a year now, despite owning multiple precision double baskets with special tampers.