To the OP - does BA still go by the policy of charging 10% of the relevant adult fare for a lap baby on a long-haul? That policy is part of why I never flew with my son when he didn't have his own seat.
As to the lounge issue, I will add my one rupee's worth as a dad of a now 10-year-old who started flying at age 2 months and now has a million miles under his belt and has earned OW Emerald status for the past 4 years.
Just because a ticket or FF status gives you the right to use a certain lounge doesn't always mean it is wise for you to do so.
The CCR is indeed a very nice facility and I'm sure your son/daughter will properly enjoy it when they reach a certain age. But I can assure you that there is nothing about the CCR experience that will appeal to your child at age 23 months, and I can assure you with equal certainty that the presence of a young child in the CCR will not be welcomed by your fellow pax.
The Galleries lounge, which you are also entitled to use, has a wonderful children's play area. My son spent many happy hours playing in the old lounge in T4, even up until he was school age. It will be a far more enjoyable experience for your family, and you are far more likely to find suitable food offerings for your child here than in the CCR.