I misread your question, so ignore my last answer.
"I read a lot" could potentially mean either "I read often" or "I read a lot of books", but most of the time it would be interpreted as the former.
2016年4月10日
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In practice, it could mean either.
It might be rephrased as "I do a lot of reading".
The speaker doesn't specify that the reading material includes books but we might assume or understand books.
2016年4月10日
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"A lot " is an adverb here, so the emphasis is on the verb " to read". It means "much" , "often", "frequently". It's not about the number of books you read.
2016年4月10日
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I agree with the other native speakers. It could mean either.
2016年4月10日
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"A lot" modifies "books", not "read". It refers to the quantity of books that you read, not how much or how often you read.
So it means "我读很多的书" instead of "我经常读书".