During my lunch break, I usually go for a walk. If the weather is not so good (or: 'that great'), I read a book or (some) news.
No, you do not need some in your sentence. Trigger happy voters, please read the whole answer before voting on it. I'm a-gonna get to the news in a moment.
A certain (unspecified) amount, part, degree, or extent of (something) (Oxford English Dictonary, I.4.a)
It is often used before mass nouns, and news is a mass noun, at least in modern standard English.
Thus, the common opening:
I've got some good news and some bad news. Which do you want to hear first?
We could also say
Some news travels faster than other news (, namely bad news).
But, like with butter, the some is not necessary. And, by the way, you can answer the question 'What did you buy?' with 'I bought butter' or 'I bought some butter'.
Thus we have:
News travels fast in this day and age.
News travels fast in the country (rural areas).
That's news to me.
Have I got news for you...
And note, so far we have been using news in its basic meaning:
Newly received or noteworthy information, especially about recent events. (Oxford, definition 1)
Keeping this definition in mind, an example closer to your sentence of not using a determiner before news is
I read news for a living.
This sentence is not talking about the newspaper or magazines but about the stuff that newspapers report. It is still talking about Oxford, definition 1, not definition 1.1, which see.
And that stuff can be written down, so you can read it. And the guy who reads news for a living must have written sources or accounts or presentations of news to read.
And once it becomes published or broadcast, news is almost always the news. Cue Definition 1.1 in Oxford:
(the news) A broadcast or published report of news
So a native speaker gets his news (new information) from the news (new information in pubished or broadcast form). And so, a native speaker would expect the news in your sentence.
Another usage of the news is to talk about one item of news:
Have you heard the news? MJ died! We landed on the moon! The war is over! Etc!
And a response could be
That is some news.
And now the meaning of some, when stressed, means
Quite a; a remarkable [piece of news] (Cf OED).
An interesting variant of your sentence is
During my lunch break, I usually go for a walk. If the weather is not so good, I read some books or some news.
Here we are back to some meaning an indefinite amount. And, because of the dual use of some, this sentence sounds much more felicitous and non non-native. So don't ever let someone tell you that how a sentence sounds is never a factor in determining either grammaticality or "felcitousness."