The iPhone “iPhone” cannot be used because it requires a newer version of iTunes. Go to www.itunes.com to download the latest version of iTunes

Just to clarify for a complete novice, I have an iphone 5S that I am changing to an iphone 6se. The Mac is running 10.7.5 and my iphone 5s was running 9.3.1 and the iphone 6se is running the same. I have the up-to-date iTunes on my phones and my Mac has 12.2.2.25.

I get the error message "The iPhone “iPhone” cannot be used because it requires a newer version of iTunes. Go to www.itunes.com to download the latest version of iTunes". This is when I try and restore the new iphone 6se from back-up for the iphone 5S.

Is it right that actually it is the Mac's iOS that is the problem and I am being forced into using El Capitan??

Many thanks for your help.