The chances of 11 speed rings fitting an old 9 speed crank and shiftly properly are slim to none. Shimano rings certainly won't fit as they are all 4 bolt rings vs. 5 from the 9 speed era. You might be able to find third party rings intended for a 5 bolt crank (whose, I don't know) and maybe it will work. One thing is for sure is that it will cost more than a Shimano 105 or Ultegra complete crankset out of the UK.

A 2001 Litespeed nearly certainly has a BSA threaded 68mm wide BB shell meaning that bog standard Shimano outboard bearing cups will fit perfectly. If you order a groupset just be sure to get the BSA cups and not Italian threaded cups or cups meant for a press fit BB shell.