What part are you struggling with and I will try to explain ?
It is nearly impossible to work out the expense of each Centre of Excellence player but you can have a full cost for the whole department per year.
As each league club gets funding for their Centres, the majority of the costs dont actually fall to that club.
Although clubs do top up this grant if it doesn't cover the total cost, TLO seemed to think that the clubs put in the lions share, they dont.
Any costs that you calculate for Lynch's development is a red herring really because the majority of the costs are covered by the annual grant anyway and not from the clubs own coffers,
I hope this is clear.
I'm struggling because you're providing no evidence - post the figures then !
It's strange that the league would appear to diagree with you - there are rules about paying a reasonable sum for players that have come through the youth system - persumably because it costs clubs a reasonable amount to develop them.