No, there is no legal limit as to how high a landlord can raise a tenant's rent outside of NYC, BUT, to be legal, the landlord HAS TO at the very LEAST give the tenant a written thirty-day-notice of intent to raise the rent. Most landlords give this 30-day nice of intent when they pick up their rent on the first of the month, with the new rent amount going into effect on the first day of the following month. A landlord can and probably should though, give longer than thirty days, say 45 or 60, to give the tenant time to think, plan and perhaps find a cheaper apartment,if they can find a cheaper place.
It has been my experience in all my years of renting apartments here in the Mohawk Valley that if you have a clean and quiet tenant who pays his/her rent on time almost all of the time, and that tenant isn't a trouble maker or calling you all of the time about every issue under the sun relating to life at YOUR rental property, you'd be a damn FOOL to raise that person's rent any more than $25.00 per year(because of property tax increases), if at all!
It could be that your friend is a problem tenant and her landlady is trying to coax her to move elsewhere without actually evicting her, which is usually when things turn extremely nasty between a landlord and tenant, in my experience. Or perhaps your friend's landlady wants the apartment to go to a friend or family member, but still doesn't want to do a formal eviction. Heck, an increase of $125.00 per month IS excessive all at once, so I believe I WOULD move rather than pay that much more every month, all of a sudden.
So, the landlady has to give her at least a FULL thirty-day written notice before any increase could go into effect. But then your friend HAS TO give her landlady a FULL written thirty-day notice of HER intent to move out if she can't afford to or just doesn't want to pay that much more in rent, in order to protect her security deposit and its return.
Hope this helps