Because this is how you ask someone in Dutch if they will turn off the light.
Dutch often uses the present tense where you need to use the future tense (will + infinitive) in English.
I'd say that "Would you turn off the little lamp?" should be accepted too, if it isn't already. Admittedly, this sounds more polite and has a more accurate Dutch equivalent in Zou jij het lampje uit willen doen?, but if I'm not mistaken, there's a difference between English and Dutch when it comes to polite or formal questions.
In Dutch, polite questions with zou are almost exclusively used in formal contexts, while English tends to use "would" and other such polite constructions in more intimate situations too. Considering that you might use this question to, let's say, ask your husband to switch off the light, Dutch would definitely not use zou, but I feel that in English both "will" and "would" are possible, despite the fact that the context is not formal at all. In fact, I even think that "will" sounds a bit too blunt.
Im translating it as will you put the lamp out as this is colloquial english .is it not acceptable?