I have Lion OS X 10.8.5 and my browser can not support it ?

Hi,

Lion is OS X 10.7. Mountain Lion is OS X 10.8.

Upgrade tyour Mac to macOS Sierra > MacOS Sierra - Technical Specifications

mac OS Sierra General Requirements

• OS X 10.7.5 or later
• 2GB of memory
• 8.8GB of available storage
• Some features require an Apple ID; terms apply.
• Some features require a compatible Internet service provider; fees may apply.

Hardware Requirements: iMac (Late 2009 or newer)

That way Safari will be updated to version 10.1.1 automatically.

Sierra is free and available for download from the App Store. Make sure to backup all your important data prior to upgrading.

For third party software compatibility upgrading OS X, see App Compatibility Table - RoaringApps.

Here are the actual requirements: How to get macOS Sierra - Apple Support. You will note that you must first upgrade to El Capitan before you can upgrade to Sierra.

To upgrade to El Capitan you must have Snow Leopard 10.6.8 or Lion through Yosemite. 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.

You can only upgrade Safari by upgrading OS X. Are you saying you cannot upgrade OS X? If your computer can be upgraded to 10.8.5, as you say, then you can upgrade to El Capitan and possibly to Sierra if you meet its requirements: How to get macOS Sierra - Apple Support.