Genki (second edition) gives the following example sentences using たくさん, but doesn't explain any distinction regarding word order:
私は京都で {写真をたくさん / たくさん写真を} 撮りました。 I took many pictures in Kyoto.
and
{野菜をたくさん / たくさん野菜を} たべました。I ate a lot of vegetables.
How does the word order affect the meaning of the sentences? Here is my best guess at understanding the distinction. For the first sentence, 写真を撮る naturally imply each other, so there is probably less distinction, but たくさん写真を撮る implies a large number of pictures, whereas たくさん撮る implies a lot of time or effort put into the act of photography.
However, たくさん食べました implies that you ate a lot, whereas たくさん野菜を食べました means that you ate a significant quantity of vegetables.
Thus, I take it たくさん can emphasize a lot of an action, or a large amount of a subject. But I take it that since it is an adverb, is not really modifying the subject, but the predicate clause.
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