The Fansite Item Lottery dont generated inflation, that's another thing in the market.
One of the most basic rules of market/economy is the law of Demand and Offer.
In microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted. It forms the theoretical basis of modern economics.
Source: Supply and demand (Wikipedia)
With the same Demand and Offer the price for the sevice or item keeps equal
If the Demand if high than Offer the price of the service or item growth
If the Offer is high than Deman the price of the service or item decreases
Demand = People who want exchange money for that service or item
Offer = People who give that service or item in exchange of money
In a very short adn simple answer:
Fansite Item Lottery = More Fansite Items In Market
More Fansite Items In Market = Growth of the Offer
Growth of the Offer = Price reduction
PD: To the end the rumors are parte of the movement of the economy, soooo yes the rumors about a new Fansite Appreciation Day affect the price of the Fansite Items.