MacBook Pro - A1286 - Update macOS from X Lion 2013

I went to EveryMac.com, selected the MacBook Pro page, then chose the oldest that featured an i7 processor, then scanned down the list until I found one with 2.0 GHz clock speed. Then scanned further down to see that no others also matched that description, and they did not.

There is a much for a later MacBook Pro 2013 model, but that one shipped with 10.9 as shipped in the box MacOS, so it can not run 10.7 Lion.

A1286 describes any of 22 15-in models issued from 2008 through 2012 that have a very similar body style. All appear to be able to run at lest 10.11 El Capitan, and that is what you should try to install next, because it includes 'modern' web encryption.

what model-year is yours?

if you used a web browser you needed to follow these explicit directions:

1. Use these links to download a macOS disk image (.dmg) file.
2. Double-click the .dmg file to open it and see the package (.pkg) file within.
3. Double-click the .pkg file, then follow the onscreen instructions to install [read: PLACE ] the macOS installer into your Applications folder.
4. Open your Applications folder and double-click the macOS installer, named Install [Version Name]. Follow the onscreen installation instructions.

that looks like early 2011 model, MacBook Pro 8,2

https://everymac.com/systems/apple/macbook_pro/specs/macbook-pro-core-i7-2.0-15-early-2011-unibody-thunderbolt-specs.html

That MacBook Pro can run up to MacOS 10.13 High Sierra.

Once it gets settled, if you like it, you could upgrade the RAM memory to 16 GB, and upgrade the drive to an SSD drive.

so if I believe the procedure I posted, you have now PLACED the Installer in your /Applications folder, and are ready to actually INSTALL the new version.

Next step should be to double-click the 'Install macOS Sierra...' item in your /Applications folder.

You should see the Sierra icon in a circular preview, show the drive on which it proposes to Install, and it should invite you to Restart to begin the installation of MacOS Sierra.

if you see a different preview or the Installer has a different name, that is a problem

if it is running any version of MacOS...

 menu > about this Mac

... but don't post your serial number, it attracts vermin.

Please do not start with the presumption of failure. Be Upbeat!

Check Your Service and Support Coverage - Apple Support

That computer will run much better with more than 6GB or RAM, which is the starvation point. More will be slightly more responsive.

If you has asked, Readers would have responded that your 2011 model can accept up to 16 GB RAM in two 8GB DIMMs, but they must be EXACTLY the correct DIMMs. Best practice is to buy from a Mac-centric vendor who can promise:

"It works in your (exact model) MAC,

or your money BACK!"

it costs them money and aggravation to get it wrong, so they get it right instead.

In the US, these vendors:

http://MacSales.com (OWC) is still the most-recommended supplier here, because they have good return policies and a lab full of Macs. They pride themselves on their service, so they do not sell stuff that is so "difficult" it needs a lot of hand-holding to get working.

OWC sells their own private-label SSD drives, which are pretty good and reasonably priced, and you know they will work in your Mac.

Look for the "My Upgrades" link on their main page, and it will lead you to parts that will work in your specific model Mac.

http://DataMemorySystems.com is less often recommended, but very close in service and real-world testing, and has historically been a little cheaper for comparable products with the same terms.

http://crucial.com is often recommended because they have a great track record of supplying stuff that works first time, every time. Personally, I am not as fond of them because they use their database of what sales "stick" rather than a lab full of Macs to obtain their results. Their recommendations tend to be more conservative than others, and they sometimes discontinue parts for older Macs before other sites do.