The 2010 Macbook Pro (MBP) shipped with Snow Leopard (10.6). If Lion (10.7) was installed then it must have been purchased from Apple and installed by the previous owner. I think that the verification problem is trying to determine if you own/purchased Lion to permit the download. The verification is done by checking your Apple ID.
In order to purchase Lion you need a working bootable Mac with access to the App Store and capable of running Lion. It's a problem because you can not meet all of those requirements at this time.
Lion purchase information from Apple:
Apple Store Search Results
www.apple.com
A 2010 MBP can run from Snow Leopard (10.6) to High Sierra (10.13).
2010 MBP information. (I did not know your MBP screen size so I picked 15"):
Technical specifications for the MacBook Pro "Core i7" 2.66 15" Mid-2010. Dates sold, processor type, memory info, hard drive details, price and more.
everymac.com
Now how to move forward. You need access to another
working bootable Mac capable running Snow Leopard (10.6) to High Sierra (10.13).
or
Purchase a bootable USB installer from Amazon or eBay.
If your MBP still has a spinner HDD & the stock 4GB RAM then I would recommend El Capitan (10.11).
Download and install current or previous versions of the Mac operating system on compatible Mac computers.
support.apple.com
If it has been upgraded to a SSD & 8GB of RAM then go for High Sierra.
Download and install current or previous versions of the Mac operating system on compatible Mac computers.
support.apple.com