Thank you Jeremyvnc!
I solved my problem. By default, the baud rate on the Bluetooth Silver Mate is 115200 (not working on Lilypad).
So, I tried to change the baud rate on Bluetooth Silver Mate (http://electronics.stackexchange.com/questions/15027/how-do-i-change-baud-rate-for-bluesmirf-without-connecting-to-pc
, this is for BlueSmirf but works perfectly on Bluetooth Silver Mate too) to 9600 and all works correctly.
I also tried to set the baud rate to 115200 using an Arduino Uno instead of a Lilypad with the Silver Mate connected and it all works (updating C# program and firmware).
Thank you very much!