Well, as far as a rule can be said to exist, I think the mavens are unanimous that 'lbs.' isn't really right. The Chicago Manual also doesn't even allow it as an option.
That said, though, I confess I use it myself in ordinary casual writing. The Chicago Manual does note in the next section, on abbreviations for units of time such as sec., min, h./hr., d./day, mo., yr., that 'In nontechnical writing, plurals of these abbreviations, unlike those of length, area, weight, and the like, are often formed by adding an s.'
In my opinion, 'lbs.' falls in the same category. No one thinks 'libra' when they see 'lb.' anyway, just as we don't think 'exemplia gratis' or 'id est' for 'e.g.' and 'i.e.' We read 'lb.' mentally as 'pound,' so we naturally want to see an S for 'pounds.'
Another similar one is 'yd.' for yard; we naturally write 'yds.' for the plural. Why we never feel the need to do that for oz., in., or mi. is an interesting question.
The same is true for 'hrs.' (surely the most normal abbreviation for 'hours') and 'yrs.,' which are both so common as to be unremarkable. I personally am less inclined, for some reason, to write 'secs.,' which Chicago also puts in the same category; but in its place I would definitely list 'mos.' (months), which Chicago doesn't even mention but which is also widely used.
I wonder if could actually be something phonetic, to do with the final consonant: pounds, yards, hours, years. It seems helpful, somehow, to have that semi-visible in the written form -- though I'm not sure the same applies to months. Maybe one of the linguistics buffs among us has an idea.
Just from the point of view of practicality, though, I think it could indeed to be helpful for LEO to list
as possible variants, even if it's necessary to mark some of them as [coll.]. I imagine tens of thousands of people beginning to learn English would be very puzzled to come across one of those in a text and not get anything at all if they typed it into LEO.