A construction may be stylistically odd without being wrong. (And we could find ordinary speakers using that construction when discussing different recommendations to be given to different people.)
So to do some further investigation, I went on Google Ngram to see which usage is more common, here's a link to what I searched:
https://books.google.com/ngrams/gra...1800&year_end=2019&corpus=en-2019&smoothing=3
I couldn't figure out how to compare Example 1 with the other three, but I think we all agree that it's correct so we don't need to discuss it.
Anyway, it looks like example 4 is far more common than example 3 (as I expected), and is even more common than example 2. I think this is pretty strong evidence that "recommend me a book" is natural enough to use.
Maybe another interesting observation is that example 2 is used more than 4 in the period 1962-1982, which coincides quite well with when the Longman Dictionary of Contemporary English was written (according to Wikipedia). But that's 40 years ago, and grammar changes with time.
On the other hand, if we replace "me" with "her", examples 2 and 4 appear with about the same frequency, with example 2 actually appearing more frequently in the past. So maybe adding a "to" would be better in the specific usage this chapter had ¯\
(ツ)/¯
I'd be interested if you can find any occurrence of "to me recommend a book/whatever" in the wild though, since Google Ngram isn't turning up any results.