1) I freaking
love August. Such a great name! My fave boy's name in fact :P
OK, now that that's out of the way-- first off, I just want to say that I think Lydia would go better in a sibset with August. August, even though it's got more ancient associations, sounds more modern and even though Hazel is gaining in popularity, I think it still sounds really old fashioned and would just be a bit odd with the more modern August. Plus Lydia has the same ancient yet modern thing that August has.
Either name's popularity doesn't matter much. Once you get past 50 or so, it's not really an issue. You might meet a few, but it won't be like they'll be one of five in a class, you know? There were 3,220 Lydias named last year, and 2,039 Hazels, and that's out of what--like over 100k girls born. So, in that regard, you should be totally fine. The names we consider "dated" tend to be the ones that were in the top 10/20, and I don't see Hazel or Lydia making the jump that high tbh
Now talking dated... Hazel does feel more dated to me, cause it really reached a high popularity (peaked at 18 in 1897) and then just about vanished, and I'm sure more than few of us can say we've got a great grams or great aunt or some other older relation with the name. That's why I see it as a grandma name. Lydia doesn't have that association so much cause while it peaked it went up a down a bit over the years and never really vanished, so it's more of a classic name to me. If anything, Hazel has a hipster vibe to it, cause of that John Green novel, though now it's being made into a movie so... maybe not so much hipster by next year, and more trendy. If either name runs the risk of being dated, and that's something that worries you, then it'd definitely be Hazel.
My PNL = http://www.behindthename.com/pnl/37275
Top: Henry & Lara (main) / Caspian & Briar (GP) / James & Georgiana (top25)
Bottom: Randall & Memphis (main) / Dinadan & Melpomene (GP) / Owain & Itonia (top25)