I have a friend who is allergic to yeast so I'm looking for a way to make a pizza dough with baking powder instead of it. Should I add a bit of lemon juice to counteract the baking soda?
You can make yeast free pizza base using baking powder, it will be a bit crumbly, but it works fine. You could use baking soda, but then as you state you need acid to react with it. Using lemon juice is an option but I would recommend against it as you don't know the exact amount of acidity you'll get and your crust will taste lemony which you don't want. Go get some baking powder instead and use about 3/4 tsp of powder per cup of flour.
You'll want to knead your dough to develop the gluten, otherwise the base will just fall apart.