The version of Safari that you are using in Mac OS X Lion is grossly outdated. It is very likely that a secure connection will not be forthcoming. For the same reason, a secure connection to the App Store is also failing. There is no security update available for that Safari version. The only way to upgrade Safari to a more secure version will be to upgrade the OS to something newer.
There are other browsers available, but the OS is too old for the most recent and secure versions of those browsers to be compatible.
I believe your best option will be upgrade that Mac to Mojave and take advantage of the more recent and secure versions of Safari. If possible and if you have no 32-bit software that would be incompatible, you should reinstall Catalina and leave it at that.
Your 32-bit apps won’t work in Catalina, Big Sur or Monterey.
https://support.apple.com/en-us/HT208436
Use the free utility Go64 to check the compatibility of your apps:
https://www.stclairsoft.com/Go64/