How do i upgrade from lion to mountain lion in 2016?

Your only choice is El Capitan unless you already have downloaded something later than Lion. See the following:

Upgrading to El Capitan

You can upgrade to El Capitan from Lion or directly from Snow Leopard. El Capitan can be downloaded from the Mac App Store for FREE. To upgrade to El Capitan you must have Snow Leopard 10.6.8 or Lion installed. Download El Capitan from the App Store. Sign in using your Apple ID. El Capitan is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

Macs that can be upgraded to OS X El Capitan

1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later

2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later

3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later

4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later

5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later

6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later

7. Xserve (Early 2009) - Model Identifier 3,1 or later

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

Are my applications compatible? See App Compatibility Table - RoaringApps

You can still get Mountain Lion, but it is also out of date and not receiving security updates. El Capitan is a more secure choice.

Mountain Lion

You are welcome.

Eric,

I am a little confused here.

I am not sure when security updates ended for OS X 10.8, but I have been running OS X 10.8.5 since January of 2016 and I did receive a security update for 10.8 sometime around April this year and it, also, applied to OS X 10.9-10.11, as well.

I haven't seen any new security updates since April, but I am still receiving regular iTunes updates, as well, and just updated to iTunes 12.4.3 as of today on OS X 10.8.5.

I was not aware of the 10.8 security update, but based on the recent Apple pattern of maintaining older operating systems, the update was/is unusual as far as I know. iTunes updates that are compatible with older OSs are not as unusual. Sorry I don't have a better answer.

Apple typically supports iTunes for a year or two after they discontinue the OS, so that is why you are still receiving iTunes updates. I don't see a security update released for Mountain Lion in April according to Apples downloads page. It is possible that your computer missed the update and it finally recognized that an old security update was available back in April. On Wikipedia it says that Mountain Lion is no longer supported as of Sep of 2015, so I don't think Apple is still pushing out new security patches. I may be mistaken though about the security update though 😉.