I'm not sure why more companies don't choose to go the direct listing route (like Spotify). Set a reference price, but allow the employees and market decide.
Tech companies especially have enough employees that own shares and want to sell that liquidity should not be a big issue. This allows the price to be tested while slowly adding volume (as price stabilizes, more employees willing to sell).
Even if you make it a lottery, you will have to make sure everybody who would want to buy at the low price gets equal opportunity to do so.
Finally, I would think the tax department could see selling at a price that you know is significantly below market value as a gift that is taxable.