Here is the menu at the Tambu Lounge for food, it is listed under "dinner"
Crisp Breads and Dips
Assorted Breads served with Sun-dried Tomato Pesto, Roasted Red Pepper Hummus, and Baba Ghanoush
$5.99
Pulled Pork Nachos
Polynesian Chips topped with Pork, Cheese, Pineapple Salsa, and spicy Mayonnaise
$8.99
Pork Sliders
Mini Sandwiches with our Kona Coffee Barbecued Pork topped with Slaw
$8.99
Beef Satay
Mini Skewers of Grilled Beef served with a Chimichurri Sauce
$8.99
Chicken Wings
Choice of Honey-Coriander Wings or Spicy Wings served with Blue Cheese and Celery
$8.49
'Ohana Bread Pudding
A single serving of our classic 'Ohana Bread Pudding served with a scoop of Vanilla Ice Cream and a side of Banana-Caramel Sauce
$4.99
So yes, you can get it. Also I don't think any eatery is off limits to kids except for V&A. Yes it is a "lounge" but it is at Disney. just don't buy your kid a lapu lapu.