I'm thinking about trying Opera, but the latest version (38) works only for Mac OS X 10.9 and newer.
I've been dancing around Opera's website but cannot get a handle on which version is the latest one which can use Mac OS X 10.7.5. I would think it'd be 34 or 36 or 37. Can someone provide that info? (Otherwise I can just download all of those and see which ones work.)
Any cautions or other intelligence on the Opera browser would also be gratefully received.

AFAICT, Opera version 37.0.2178.54 is the last one for Lion, before version 38.0.2220.29 moved the System requirement up to Mavericks. Unfortunately my use of Opera is rather rare, plus I’m not running Lion, so I don’t have any useful tidbits for you there, sorry.

Many thanks. That saves me some time and effort.
The only reason I thought of experimenting with Opera is that there's one secure website that takes close to forever to load in Firefox and Safari and even then more often than not refuses to let me log in. We shall see.

Well, I'm getting closer to accessing that secure website.
I installed the last Opera 37 version which would work for Lion and was able to acquire the secure login page, after which it just crapped out.
When I checked with that website's tech support, they suggested that I try Google Chrome (even though I pointed out that it was apparently based in large measure on Opera).
So I'll give that a shot, assuming I can find the version which works for Lion.

By the bye, Opera has one of the strangest GUIs I've come across: Something called Speed Dial shows up as the home page which seems to be impossible to program otherwise. And there seems to be no reload function.

Browsers change layout engines from time to time so it can be tedious to compare one browser with another. According to this Wikipedia article up to version 37 Chrome used the same Webkit layout engine as Safari but since then they have switched to the same Blink layout engine that Opera has used since Opera 15. Of course Firefox uses the Gecko layout engine developed by Mozilla.

But the type of issue you are having is more likely related to the ECMAScript (a.k.a. Javascript) engine. Chrome uses the V8 javascript engine as does Opera since version 15. Spider Monkey is used in FireFox and Safari uses JavaScriptCore. Theoretically all the ECMAScript/Javascript engines conform to the ECMAScript standard there are variations within the standard and there are extensions and versions of the standard that are not universally supported.

Wikipedia has a Comparison of layout engines (ECMAScript page. Since ECMAScript was a Mozilla brainchild it is not surprising that the broadest ECMAScript support is found in the Gecko layout engine used in the FireFox, SeaMonkey, and Camino browsers. So if all else fails on the site you are trying to access I would recommend you try one of those three. Taking the chart of layout and ECMAScript engines together with the browser versions that will run on your Mac you should be able to deduce the various combinations of layout and ECMAScript engines available to you. Unfortunately because of your somewhat elderly version of OS X, the site may be using an ECMAScript command or option that is not supported in any browser/layout engine/ECMAScript interpreter that will run on your Mac. What was it Virtual1 said in another thread about "...dragged kicking and screaming into the present"?

So much for the idea of trying out Google Chrome. Google stopped supporting anything for Mac OS X less than 10.9 last fall.
{sigh}
Moving right along ....

Leaded gas is also getting really hard to find

Seek and ye shall find ... additives to make up for same.