Output VAT on lottery grants

Bit of a mental block here: I'm aware that a local authority grants may or may not be a business activity and therefore may or may not be VATable in the hands of the recipient. I'm also aware of the Wolverhampton CAB case on this, and VAT notice 701/1. If the grant is considered to be a business activity, the recipient organisation can register for VAT, bill the local authority on a VAT invoice and recover input VAT.

However, if the grant comes from the Lottery (a) can it ever be a business purpose, and if it can (b) is VAT charged on an "invoice" to the Lottery when claiming the grant?

Thanks for the help -

Alan
Alan Burton