The easiest way to go low carb when eating out is to ask for a bunless burger. Load it up with salad, mayo, cheese, pickles ...
If adding a diced red onion, pre cook it by frying in a little butter until soft then add to a bowl with the mince/ground beef.
Divide the mixture into 5 portions. Take each portion of ground/mince beef, and squeeze it into a firm, flat burger shape. The firmer you squeeze it into shape, the more likely it is to stay together while cooking.
*Optional - add a small red onion finely diced to the beef burger patties mix before cooking
*You will need to calculate your vegetables separately as what and how much you choose will vary enormously.