I know this might be very late in response to this thread, but I have been struggling with this toolkit, a bluetooth mate silver, and a lilypad simple (328) for a couple weeks now.
I believe I have a (very simple) solution, basically to turn down the baud rate of the bluetooth mate. You need to connect to the Mate using the default baudrate (115200 for the mate) either through the lilypad or even remotely after hooking the dongle up to 5v, enter command mode ("$$$"), change the baudrate to something slower (e.g. "SU,57" will change to 57600), then restart the dongle ("R,1"). Although 115200 works with the bluetooth and lilypad in other simple scenarios, I suspect that the clock speed simply isn't quick enough for this toolkit.
We discovered this solution after seeing that the MultiColorLamp solution worked perfectly with the Arduino Uno, but not with the Lilypad. After changing the baudrate to 57600, the lilypad worked as well.
Another caveat (I'll throw this in for free!); the Bluetooth Mate Silver/Gold require at least 4.5V to run. The included 3.7V Li-Po battery with the Lilypad Simple will not power the bluetooth. Some sort of external power needs to be hooked up to the Lilypad via +/-.
Hope that helps someone :)
-Alper