Peejay,
As you rightly note, the answer to your question is in the lease. Rising damp is likely due to deficiencies in the exterior damp course. So it is very likely to come out of the maintenance budget.
You don't say where you are in the block but I presume not on the ground floor. People on the top floors are equally very grateful that they do not have to pay for roof repairs I bet.
The fact that you have your share of freehold will make little difference. It is times like this that the lease document comes into its own.
If you have a managing agent then it would be worth checking with them.
If you don't have a sinking fund to draw this out of or don't have arrangements for overpayments on your maintenance then "surprise" items like this will always be unwelcome.
For more detailed advice on leasehold then have a look at the Association of Leasehold Enfranchisement Practictioners web site at www.alep.org.uk.