Here’s an instance of the phrase greater or lesser:

Unobjectionable, right?
Here’s another instance:

Unobjectionable too, no?
Here’s another example of the same sort:

That’s unobjectionable too, right?
Actually, the second and third examples don’t work.
The first example refers to something getting bigger or smaller. So in that context, greater means “bigger” and lesser means “smaller”. By contrast, the second and third examples compare something to something else. In that context, greater, when followed by than (either immediately, as in the second example, or more remotely, as in the third example), is used to mean more.
In other words, the word greater works in both contexts. But lesser doesn’t work in the second context. One doesn’t say lesser than; you say less than. Nevertheless, today I encountered this ungrammatical use of greater or lesser in a contract I was asked to review, and I found more than 1,700 examples on EDGAR. And I found a bunch more examples of lesser than on its own, without greater. So this ungrammatical use of lesser than would seem to be a thing.
I recommend if you have a following than, use more or less instead of greater or lesser (and instead of the grammatical greater or less too). (And if lesser than is used on its own, use instead less than.) If instead you’re referring to something getting bigger or smaller, greater or lesser would do, but bigger or smaller is simpler, so I suggest you use that instead.
Is anything at stake here? Not in terms of the deal, but I’d have thought we wouldn’t need any arm-twisting to convince people that it’s best to fix ungrammatical writing.

Surely you know by now you’re wrong a out the arm twisting, right?
Hi Rob. Arm-twisting is never going to work. I think it’s a matter of whether someone recognizes that something is ungrammatical.
Ken:
In the second example, even “greater or less than” sounds unidiomatic to my ear. I don’t think of time periods as being “greater than” — I’d have said “longer or shorter than.” Same with “more or less than” with respect to time. I would say “a week is longer than a day” rather than “a week is more than day.” But I might say “a month is more days than a week.” I dunno.
Chris
Hi Chris. For purposes of comparing something to something else (in other words, if you need “than”), perhaps two factors are relevant. First, is whatever is being measured a mass noun or a count noun? Next, is what is being measured time or something tangible? If it’s a count noun (including “days”), you can always use “more or less than”. If it’s a mass noun (including “a period” and “a quantity”), you use “longer or shorter” for time and “more or less” for that which is tangible. But I’ll think about this some more.
In the second example, I don’t see how anything is lost by saying “other” and in the the third example, “different…from.” Since both are referring to countable things (in the first example, “a number” isn’t countable, only sizeable), the only possible differences are of quantity.