How can I be sure that the information about winnings and the number of tickets sold is correct? Is there any tool that can be used to check this
information?

There is a Statistics tab in the lottery menu. This tab contains information about the number of tickets sold, numbers drawn, jackpots and winners’ wallets (showing how many numbers were matched and what the payouts were). This information can be verified through Etherscan and the program code shared on GitHub.

More information you can find in Whitepaper