According to Frank Seravalli, the 2025 NHL Draft Lottery will take place on May 5th. No official time has been announced. The draft lottery typically takes place right before a primetime playoff game.
The Philadelphia Flyers currently have the fourth-best odds of winning the draft lottery, 9.5%. Here are the rest of the odds:

For those who do not know, the NHL Draft Lottery has two drawings. One for the first overall draft selection, and one for the second. Teams that win the lottery can move up a maximum of 10 spots, which is why Detroit and down cannot win the top pick.
Once the two drawings are done, the rest of the draft order fills out based on the final standings.
This is why the Flyers can, at worst, pick at the No. 6 overall spot. It is also why the Flyers have the best odds at landing the No.5 overall pick. If one team behind the Flyers wins the NHL Draft Lottery, the Flyers then pick one spot behind.
After May 5th, the Flyers will be able to start using their surplus of draft picks to move back into the lottery, if that is what they choose to do.
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