If anyone's interested - I think there's a problem with the Lilypad bootloader. It reports a 00 00 00 signature whereas the ATmega168 is expected to report 1E 94 06.
What I was trying to do is run a lone ATmega168 chip with the absolute minimum number of components required with FTDI, i.e. the reset pull-up and DTR capacitor. No resonator or crystal, which is why I selected the Lilypad as board before burning a bootloader into the chip via ISP.
On Mac, here's what I did to test this: - cd /Applications/arduino/examples/Communication/ASCIITable/applet - /Applications/arduino/hardware/tools/avr/bin/avrdude -F -p m168 -P /dev/tty.usbserial-A900a4Pz -c avrisp -b 19200 -U flash:w:ASCIITable.hex
So it works, i.e. you can run a bare ATmega chip with just one resistor and one capacitor plus an FTDI cable or breakout board - IF you disable the signature check in avrdude with -F, that is.
FWIW, the error from the Arduino-0013 upload was: "avrdude: Yikes! Invalid device signature."
Suggestion for the next Arduino IDE release: a slightly adjusted Lilypad bootloader?