These ARM Teensies are now supported through ChibiOS.
You'll need to install an ARM toolchain, for instance from gcc ARM embedded website, or using your favourite package manager. After installing, you should be able to run arm-none-eabi-gcc -v in the command prompt and get sensible output. This toolchain is used instead of avr-gcc, which is only for AVR chips. Naturally you'll also need the usual development tools (e.g. make), just as in the AVR setting.
Next, you'll need ChibiOS. For Teensies, you'll need code from two repositories: chibios-main and chibios-contrib.
If you're not using git, you can just download a zip of chibios from here, unpack the zip, and rename/move the unpacked directory (named ChibiOS-<long_hash_here>) to tmk_core/tool/chibios/ChibiOS (so that the file tmk_core/tool/chibios/ChibiOS/license.txt exists). Now the same procedure with a zip of chibios-contrib from here: unpack and move ChibiOS-Contrib-<long_hash_here> to tmk_core/tool/chibios/ChibiOS-Contrib.
If you're using git, you can just clone the two repos inside tmk_core/tool/chibios: chibios and chibios-contrib.
(Why do we need chibios-contrib? Well, the main repo focuses on STM32 chips, and Freescale/NXP Kinetis chips are supported via the Contrib repository.)
This should be it.
Running make in keyboard/teensy_lc_onekey should create a working firmware in build/, called ch.hex.
For more notes about the ChibiOS backend in TMK, see tmk_core/protocol/chibios/README.md.
It's set up for Teensy LC. To use 3.x, you'll need to edit the Makefile (and comment out one line in mcuconf.h). A sample makefile for Teensy 3.0 is provided as Makefile.3.0, can be used without renaming with make -f Makefile.3.0. Similarly for Teensy 3.2, there's Makefile.3.2.
TMK itself is written by hasu, original sources here.
The USB support for Kinetis MCUs is due to RedoX. His ChibiOS fork is also on github; but it doesn't include Teensy LC definitions.
Currently only the more fancy suspend features are not there (power saving during suspend). The rest should work fine (reports either way are welcome).
The notes below explain what commands can be used to examine and set the status of Teensy pins.
Each pin sits on a "port", each of which comprises at most 32 individual pins. So for instance "PTC5" from Kinetis manual/datasheet refers to port C (or GPIOA), pin 5. Most functions dealing with pins take 2 parameters which specify the pin -- the first being the port, the second being the pin number.
Within ChibiOS, there are definitions which simplify this a bit for the Teensies. TEENSY_PINn_IOPORT represents the port of the MCU's pin connected Teensy's PIN n, and TEENSY_PINn represents its MCU's pin number.
A MCU pin can be in several modes. The basic command to set a pin mode is
palSetPadMode(TEENSY_PINn_IOPORT, TEENSY_PINn, PAL_MODE_INPUT_PULLUP);
The last parameter is the mode. For keyboards, the usual ones that are used are PAL_MODE_INPUT_PULLUP (input with a pullup), PAL_MODE_INPUT_PULLDOWN (input with a pulldown), PAL_MODE_INPUT (input floating, a.k.a. Hi-Z), PAL_MODE_OUTPUT_PUSHPULL (output in the Arduino sense -- can be then set HIGH or LOW).
Pins are set HIGH (after they've been put into OUTPUT_PUSHPULL mode) by
palSetPad(TEENSY_PINn_IOPORT, TEENSY_PINn);
or set LOW by
palClearPad(TEENSY_PINn_IOPORT, TEENSY_PINn);
Toggling can be done with
palTogglePad(TEENSY_PINn_IOPORT, TEENSY_PINn);
Alternatively, you can use
palWritePad(TEENSY_PINn_IOPORT, TEENSY_PINn, bit);
where bit is either PAL_LOW or PAL_HIGH (i.e. 0 or 1).
Reading pin status is done with
palReadPad(TEENSY_PINn_IOPORT, TEENSY_PINn);
The function returns either PAL_HIGH (actually 1) or PAL_LOW (actually 0).
All the commands that are available for pin manipulation through ChibiOS HAL are documented in ChibiOS PAL driver docs.