There is no direct upgrade from Lion to High Sierra, as the latter expects one to be running Mountain Lion (10.8) or later. You can go directly from Lion to El Capitan (10.11), and then upgrade from there to High Sierra. For current browser security consider Firefox 108.0.2 or the current Brave browser supported in Sierra or later. Safari in High Sierra is long out of date.
I recommend first backing up the MacBook Air to Time Machine and setting that drive aside. Your third-party applications, printer, and scanner drivers will likely need to be updated from the respective vendors for High Sierra compatibility. Look before you make the upgrade to be certain support remains.
Then, using the Safari browser, visit How to download macOS - Apple Support and note the special instructions for obtaining the El Capitan installer.