Only when you emphasize that there is only one single book that you read do you say 'bir kitap'. In this sentence you want to say that you are reading. The Turkish sentence could be translated as well ' I am reading books next to the lamp' Only if you want to state that it is a book and not a newspaper that you read you would say 'bir kitap' Ben kitap okurum. = I read a book or I read books
It cannot be "the book". In that case the sentence would be "Lambanın yanında kitabı okuyorum.' (kitabı = acc. object). If it should be "a lamp" it would be "Bir lambanın yanında kitabı okuyorum" I am nor native English speaker nor native Turkish speaker. Sorry, I cannot explain it better.