LRN bullets have been around since cartridge guns were invented. The .38 Special arrived around 1899/1900 in both smokeless and blackpowder loadings. The 158gr LRN bullets arrived shortly afterwards [circa 1905-1909] and were considered the "standard" bullet for the cartridge for many years.
Police agencies issued the .38 LRN as their standard ammo for many agencies up through as late as 1968. Officers who supplied their own ammo often used a LSWC for it's reputation as being a better man stopper.
In the 30's, the 200gr LRN was offered in the .38 Special. But at only ~740 fps, it was anemic and unable to penetrate autobodies. But then, the 158gr was not much better either. The soft lead deformed too quickly on impact.
In the 1950's, the 158g LRN was cheap and easily available, making it the choice for issued ammo to police. Officers who could buy their own often purchased the 158gr LSWC loads for their reputation as a fight stopper.
In the 1970's, Lee Juras (Super-Vel Corp.) came out with very light bullets (110-125gr) at higher speeds to increase the potential for expansion. These worked somewhat better than standard loads, but were hard on the guns (many were essentially +P+ loads).
In the mid 70's, LAPD reverted to the LSWC-HP with a 146 grain bullet loaded to what would be a +P standard. After about 3 years of little advantage, they returned to a standard 158gr LSWC or JHP to save money. Officers with .357 revolver were required to use .38 Special ammo due to the urban environment.
Some Highway Patrol agencies used .357's with JHP ammo and other less urban PD's used the 125gr Remington SJHP rated at 1490fps from a six-inch barrel. This round became the premier "man stopper" round. We then saw .38 Special ammo in 125gr become popular too because the lighter weight allowed faster velocities in the "standard" load (and much faster in +P loads).
Agencies that used the 158g LRN used it because it was cheap mostly. The bullet's velocity was only 750-770 fps in most loadings.
Today, I would use the LRN bullet only for targets and plinking, with an occassional use on rabbits and smaller critters.