original owner suddenly locked out from 1-year old ipad

I am the original ipad air 2 owner, suddenly locked out from my 1-year old ipad, with no options for unlocking it... PLEASE HELP!!!!

Here is the story. I bought ipad air 2 for my son 1 year ago. I originally set it up, it was a brand new device, so there is no "previous owner". Now, I don't use the device, my 12-year old son does. (i dont use any other Apple products ). One week ago my son informed me that he no longer can log in into ipad. The device is never out of the house so I am sure it has never was tempered by anyone.

-- the question, how is the login password suddenly changed on its own? How can that be?

The device was not backed up because there is no Windows or Apple computer in the house (We use Ubuntu). So, to reset the device i don't have option of connecting to iTunes, even though there is iTunes on ipad and my son even bought some games (Terraria and others), I have no clue why all this cannot be a proof that I am a rightful owner of the device...

Next... When I called Apple they said that the only thing i could do is reset the device and loose all data (no iTunes on any computer). So I did. Next thing, it is saying that the device is locked to Apple ID account with @icloud address. I've never used email from icloud so my guess is that i was led to set it up an icloud email account as a part of the process. Since i am not using any other Apple products naturally i never used this email address ever again. I am sure i saved the original setup information but unfortunately can't find it. I don't even remember the full email address as apple only show this: l*****@icloud.com.

-- What can I do at this point?

Addendum: Also, somehow my son was using his gmail for connecting with some games he was downloading, here is one such email:

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Application: SplitPic

Version: 4.3

Device: iPad Air 2 (iPad5,3)

iOS Version: 8.3

Free Disk Space: 917.61 Mb

Total Disk Space: 11.94 Gb

Sent from my iPad

Thanks for downloading Split Pic we appreciate the support! Please let us know if there is anything we can help you with.

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Alex