It is possible to make an offer for airport lounge access while you are at the airport, however it may not always be the most efficient option.
Many airport lounges have limited capacity and may be unable to review and accept your offer in a timely manner if they are busy. In order to increase your chances of having your offer accepted, it is best to make your bid as early as possible, ideally as soon as you are aware of your travel plans. This gives the airport lounge plenty of time to review and consider your offer and increases the likelihood that they will have availability to accommodate you.
Additionally, it is worth noting that some airport lounges may have stricter requirements for accepting offers made at the airport. For example, they may only consider offers made within a certain timeframe before the desired entry time, or they may have a higher minimum bid amount for airport offers. These requirements can vary by airport lounge.
In short, it is generally more reliable to make your bid as early as possible. This allows the airport lounge to review and consider your offer in a timely manner, increasing the chances that they will be able to accommodate you.