Yes. The Illinois lottery administrative rules specify the fund segregation and account requirements for lottery funds (11 Ill. Adm. Code 1770.60(t)):

All Lottery proceeds are funds of the State of Illinois, must be segregated from other business or personal funds, must be held in trust on behalf of the Illinois Lottery, and the licensed sales agent must, under penalty of law, maintain a separate bank account exclusively for deposit and transfer of weekly Lottery fund settlements by means of an Electronic Fund Transfer system.  The account must be designated on the bank's records as “Lottery Trust Fund Account.” 

Your customers’ contracts with the Illinois Lottery likely also require segregated trust accounts. The Illinois Lottery Retailer Application Packet states that a retailer that sells lottery tickets must “segregate from all of its other business receipts and funds and hold in trust all proceeds from Lottery sales, which the Retailer will deposit in a separate Lottery trust fund account . . . .”