Can a lost wifi iPad Air 2 connect to internet after set in lost mode
A Wifi-only iPad will only connect to the Internet via known Wifi networks. If you had some public Wifi networks saved (either directly on the iPad, or through iCloud Keychain), then there’s a chance your iPad will connect to the Internet, if and when the person in possession of it comes within range of such a Wifi network.

The problem is many (most?) public Wifi networks use a “captive portal” (the confirmation page asking you to accept terms of use). The iPad can’t communicate with the Internet until after tapping through the captive portal. So there’s a great chance your iPad will never connect to the Internet. In addition, thieves often enable Airplane Mode or at least disable the cellular/Wifi radios, so it’s important to set Lost Mode as soon as the device is lost.

And just so we’re clear, if you only put your iPad in Lost Mode AFTER its battery died and it hasn’t reconnected to the Internet since, then it is NOT in Lost Mode. You may have informed iCloud that your iPad is lost; however until iCloud can communicate with your iPad, it will NOT be in Lost Mode. It all depends on when you activated Lost Mode.

However since you had Find my iPad turned on, Activation Lock will prevent any potential thief from activating it and associating your iPad with their Apple ID, even if they manage to wipe it.

The real danger is if they somehow crack your passcode. Then they can access whatever you had locally on your iPad, including photos, email, etc.

So I hope you had a passcode and that it was not easily guessable. Based on what you said however, that was not the case, so whoever has your iPad would also have access to all the data currently on the device.