With LHW, you definitely always want to book through their website.

I haven't any experience with trying to claim points back after the fact, but when I was in the exact same scenario, I did ask their customer service about it before my stay. They quite categorically stated that stays booked directly with the hotel accrue no points and no benefits. I got the distinct impression that no exceptions would be allowed, but I guess it never hurts to try.

Fortunately, in my case I was able to cancel my booking with the hotel with no penalties, and re-book the same stay for the same price through the LHW website.