If the difference in charge becomes too high, air, preferable humid air will become a conductor which guides the discharge. Since many objects near the ground have a higher conductivity than air, lightning will find its the way of least resistance.
Cell phones are usually located in your pocket, handbag or near your face when calling..
Devices which run on batteries have a neutral charge regardless of turning them on or off, but are not connected to the earth like TV's via the electric plug.
Cell phones however do contain metal parts which could be dangerous, since if held nearby these parts form a conductor which could guide electricity to your body, if this would happen it would leave in the best case nasty burn wounds.
Although I'm not sure this custom still exists, interestingly enough in Isan, North-East Thailand, casualties of lightning used to be burried standing up with a metal pan on the head, instead of being cremated. Only older people who died from natural causes were cremated, but this custom has changed over time.
Back to the main topic, the advice is:
- No, there's no need to turn off your cell phone during lightning. If needed, use your time for other safety precautions
- In the safety of your home or (closed!) car, use of your cell phone would be a low risk issue.
- When outdoors don't keep your cell-phone near your body, regardless whether it's on or off.
- More importantly, don't call outdoors!
- Half an hour after the last strike, use of your phone is generally considered safe.