Question about -lity and -rity

There's a matter that's been bothering me for some time. It concerns -lity and -rity. In all the series of Gregg shorthand that I know a bit about, -lity is also used for -lty; e.g. admiralty, faculty, fealty, loyalty, penalty. But -rity seems never to be used for -rty; e.g. liberty, poverty, property, puberty. Regularity and simplicity suggest that these word endings should be used in parallel ways. Certainly no speed is gained by failing to use -rity for -rty. Does anyone on this blog know why Gregg has this asymmetry?