By the way, I do call my dogs over individually and offer them food a lot of times. And SOMETIMES I'll have multiple dogs laying in front of me (when invited) and I'll feed them tid bits, but if I tell them to go lay down, it's just like any other command.
For example, one of my Yorkies "Ava" is still being watched because I'm staying w/ my folks until my baby is born and there house is larger than she's used to. So I'm careful about her housebreaking habits and so on. Anyway, while I'm eating, not only is she near me, she's right on the sofa (if I'm eating on the sofa) laying down about a good foot or so away from me. And even then, if I offer her something, she's not allowed to come up and take it. I "give" it to her. She's quite the happy camper and one day within the next few months, I'll retrain her just like all my dogs and she too will learn what "Go Lay Down" means.