I think Samsung phones do this. I dont know for sure never owned a samsung phone, but i know girls used to get them for this purpose, so look up a Samsung phone you like and do a search on it for "privacy lock"
A long time ago now but my Motorola V3 had the capability to individually lock specific functionalities e.g. contacts, messages, menu, keypad lock etc.
Motorola L6 doesn't seem to be able to do this however. Most phones are capable of requiring a security code for either menu access or unlocking the keypad these days if you don't mind having less granular access.