Date of introduction of LHB's:
New Delhi-Lucknow Shatabdi- Nov'2001 (First shatabdi to get LHB)
Mumbai Rajdhani- Dec'2003 (First Rajdhani to get LHB)
Bhubaneswar Rajdhani- Jan'2009
Trivandrum Rajdhani- July'2011
Bangalore...
more... Rajdhani- April 2012
Ahmedabad Rajdhani- Apr'2012
Chennai Rajdhani- 2012
Ranchi Rajdhani- June'2013
Jammu Rajdhani- june'2013
These dates were noted by me in a diary last year after searching the Internet (only reliable sources used). I am not sure dates of LHBification of HWH or Sealdah Rajdhanis but it may be 2006.