Just in case there is anyone else out there who has this problem, I have now found a complete solution. I really like Linux lite (apart from the numlock on problem even when you have set it to off in the BIOS) and so did not want to have to lose it on those older "not powerful enough" PCs. The thought of having to run Ubuntu Mate or Puppy as the only option left did not appeal to me. Quite a few users have an older PC which they may keep for some mundane tasks or for back-up if their main machine fails. You can keep your "not powerful enough" old AMD XP (non SSE2) PC going with internet and a local e-mail client if you know what to do. You do not have to send it to landfill just yet.
I tried quite a few other browsers claimed to run without SSE2, but none of them did. Some started up and then soon bombed out; others would not run at all. SRware iron, QtWeb, SlimBoat, SeaMonkey, Opera, Maxthon3, Midori, Konqueror, Light, Epihpany and Palemoon (nonsse2) all failed to run. Then I had a stroke of luck. I discovered that the Tor browser, which is actually included in the 3.8 Linux lite menu on option "Lite Software" runs without any problems, and is not too slow. For me so far on these two PCs it has not crashed once. Then I discovered that the e-mail client Evolution ran without any problems, after I had downloaded and installed it via the command line from the Ubuntu repository.
So, all you need to do is delete Firefox and Thunderbird using the Install/Remove/Software option on the menu; remove the Firefox icon on the panel; install Tor from the Lite Software option on the menu; and then install Evolution on the command line from the Ubuntu repository. Then you will have a very usable old, "not powerful enough" PC running Linux lite like a dream.
SOLVED
I tried quite a few other browsers claimed to run without SSE2, but none of them did. Some started up and then soon bombed out; others would not run at all. SRware iron, QtWeb, SlimBoat, SeaMonkey, Opera, Maxthon3, Midori, Konqueror, Light, Epihpany and Palemoon (nonsse2) all failed to run. Then I had a stroke of luck. I discovered that the Tor browser, which is actually included in the 3.8 Linux lite menu on option "Lite Software" runs without any problems, and is not too slow. For me so far on these two PCs it has not crashed once. Then I discovered that the e-mail client Evolution ran without any problems, after I had downloaded and installed it via the command line from the Ubuntu repository.
So, all you need to do is delete Firefox and Thunderbird using the Install/Remove/Software option on the menu; remove the Firefox icon on the panel; install Tor from the Lite Software option on the menu; and then install Evolution on the command line from the Ubuntu repository. Then you will have a very usable old, "not powerful enough" PC running Linux lite like a dream.
SOLVED