No one has a receiver that works with a specific antenna it's a matter of what programming you can and cannot receiver based upon the antenna type.
In your case, a single LNB antenna can receive ALL of the DirecTV SDTV programming by pointing only at the DirecTV 101 satellite. You will not be able to receive any of the DirecTV HDTV programming.
Dish Network uses 3 different satellites to provide programming so you would have to pick one of the 3 and watch only the programming coming from that one satellite. Most of Dish HDTV programming comes from the 129 and about 70% of the SDTV programming comes from 119 so you might be able to find a happy medium with SD only and the 119. If you are so inclined, you could even re-point the antenna to a different Dish satellite (they use 110, 119 and 129) when you want to watch programming from a different satellite.