Tosfos (Kiddushin 59A end of dibbur hamaschil Oni – sorry I don’t know how to type in lashon hakodesh) says that one is permitted to hire a rebbe for his son who is already employed by someone else to teach that person’s son – basically stealing someone else’s hired rebbe. The first employer cannot stop him by saying go find another rebbe, because the second person can say that he can’t find someone else who can teach his kid as well as this one.
A few thoughts I’d add:
1. it would seem that a rebbe is just an example of an employee and whatever halacha applies to stealing a rebbe would apply to stealing a cleaning lady. Is there any choshen mishpat difference?
2. it would seem that according to tosfos you can only steal the cleaning lady if she is better at cleaning than anyone else out there (or maybe if there is a shortage of help out there and you can’t find another one without stealing from somebody?), not just because you’re too lazy to look for another one.
3. even according to tosfos, its muttar but perhaps he would agree that al pi mussar you shouldn’t do it?
4. a disclaimer that we can’t pasken from a tosfos. Other rishonim may disagree and the shulchan oruch and poskim may not pasken like this tosfos, I don’t know – ask your rov.
5. another disclaimer that I didn’t look at the meforshim as i don’t have any seforim here at work (I looked at the tosfos itself on e-daf), so if anyone knows that the acharonim or maybe the other rishonim explain tosfos differently then please correct me.