Updates for Safari

Upgrade the computer’s OS if possible.

(140386)

You're on a fossil version of OS X and there are vulnerabilities with the security of network connections that far back, and your choices are to upgrade to a newer version of OS X via the Mac App Store — this if your Mac supports that upgrade — or to switch to a different browser.

The Google Chrome browser currently has support for 10.7, but that support due to be retired in an upcoming release. Which leaves you with Firefox as an option, for as long as that's supported on 10.7. This if you can't upgrade to a more current version of OS X.

If you do upgrade, make a complete system backup first. Preferably to external storage. Maybe two backups. OS X upgrades generally don't fail, but your data is too valuable, and is not worth even that minor risk. Have a backup.

Your choices here are limited. Make a full backup or two to external storage (as would be recommended in general), perform the upgrade, and see how well your configuration works. Older computers that were purchased with minimal configurations have never upgraded all that well, unfortunately. Middling and higher-end configurations — what can work better, if you're planning on keeping the computer for a while — have usually done better with upgrades. With some older systems, an SSD upgrade is both feasible and can be helpful with the system performance. (Macs that are short on physical memory will run at the I/O speed of the disk storage, and an SSD is far faster than the hard disks that were typically found on Macs from seven or eight years ago.) If El Capitan does not work well enough for you, you're left with a replacement computer (or the SSD hardware upgrade), or rolling in your backup and using a different browser or a different operating system, or replacing the Mac with a new or newer used model.