The center contact of the bulb typically connects to the medium-power filament, and the ring connects to the low-power filament. Thus, if a 3-way bulb is screwed into a standard light socket that has only a center contact, only the medium-power filament operates. In the case of the 50 W / 100 W / 150 W bulb, putting this bulb in a regular lamp socket will result in it behaving like a normal 100W bulb.
Based on the above text, what's the best answer to this question: will a three way bulb work in any lamp?
yes