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.