Pixy currently uses Keil MDK-ARM. We were one of the first users of the LCP4300 series from NXP and Keil was the only toolchain with comprehensive support.
Keil is basically free for university users, but costs real money for everyone else.
To compile the firmware with Keil, you just point the IDE to the “workspace.uvmpw” workspace file in ~src/device/main_m4. It will open a workspace with 4 different projects: main_m4, main_m0, libpixy_m0, libpixy_m4. Compile the 4 projects in this order: libpixy_m4, libpixy_m0, main_m0, then finally the main_m4 project. The main_m4 project will create a firmware.hex output file that you can then upload into Pixy using firmware upload mode.
If you'd like to modify or create your own firmware using a free tool from NXP (LPCXpresso), which uses GCC, please join our firmware SDK group.