This happens to everyone,diabetic or non diabetic. If you ask anyone, they will tell you they also feel like sleeping after their meals. This happens because when you eat all the blood flows right to your stomach in order to digest the food you have eaten. This is why it is normal to have a rest after heavy meals so that your stomach can do its job properly. You just don’t worry about your sleepiness, it lasts only until you have digested the food you have eaten.
What was your pre-meal level ? Have you taken your bg levels after a low carb meal, when you feel sleepy ? What did it consist of ?