Can I power a LilyPad with an iPhone lightning port? I want to make a toy car that follows a black line on the ground by using two sensor on the left and right sides of the car both pointing down. The sensor converts the light into a voltage that I will use to make the car turn left or right. I know that I can use batteries, but I am still very curious to find out if I could use my iPhone to power an Arduino because I also want to make a case with different sensors in it, and it would be thinner if I didn't have to put a 9V battery in the case.
If the phone has an accessible battery you could conceivably use the battery terminals to power a device such as Arduino. However, I think current smartphone batteries have complex monitoring circuits so this wont work.

If it doesn't, you'd be looking at using the USB/charger port on the phone.If your phone supports USB On-The-Go, I know that it allows phones to act as USB hosts, and according to USB-OTG specifications, the host must be able to supply at least 8mA of current between 4.4V and 5.25V.

If that's enough for you it could work.