No - he came to give evidence on his area of expertise for the court of appeal, not in this case to explain the children's deaths. The court of appeal at this point considers whether there was anything wrong with the conduct of a trial.
The aim was therefore to consider how the prosecution had argued the case, based on Ben Myers's assertion that their claims had changed as they related to Lee's paper. The court needed to consider from there whether Lee's expertise would have undermined that changing argument if the defence had been prepared for it.
That is the kind of question the Court of Appeal can consider. What Lee needed to do in that case was to state whether the prosecution's arguments were compatible with the science as stated in his paper. His remit was not broad. Perhaps Myers could have found other grounds for appeal, but I doubt the CoA would have admitted fresh reports at that point. In any case, that's not the task Lee was set.
Later, he volunteered to read the medical records and investigate causes of death, as head of a panel. That's when he will have received all of the medical records.
So, to return to the original point, experts like Lee and his panel (not forgetting the UK panel too) have had access to and have reviewed all of the medical records in producing their reports on these children.
(ETA it is normal to name a medical discovery for the discoverer. Lee's sign is a convenient way to distinguish this rash from others. As far as I know it took him over 30 years to start using the name, so it looks as if his ego is less important to him here than achieving greater clarity in explaining the science)