А почему в этом случае употреблён some ? Do you want some lemonade too?

We use 'some' in positive sentences.

We use 'any' in negative sentences and questions.

But we also can use 'some' in questions:

- When we expect the answer to be 'yes' or when we are offering something.

Do you want some lemonade too? (offering)

- When we are making a request.