I've booked for lap-child/infant half a dozen times (before my daughter turned 2), although not on CX but on SQ. Still, I imagine it to be similar. Lap-child ticket is normally 10% of the commercial ticket of the class you're booked in. My daughter did not have a seat but a bassinet instead.

You can purchase the ticket at the airport in HKG. A friend of ours did that for her 11 mth old, on CX. She was advised not to use her miles for her infant as it would've been the full redemption miles. There's no lap-child/infant miles when doing a redemption, she was told.

We've been advised not to use miles too, on SQ, to redeem for a lap-child as it's not worth the full adult miles. Commercial lap-child ticket is cheap enough (If you travel often, you can save your miles and use them to redeem for a ticket when your child turns 2 and needs a seat - that's what I did. It's a lot cheaper, in my case, than paying full commercial 1st class fare for her)

Hope this helps.