The Kina Lillet Bond speaks of can be found today labeled as White or Blanc Lillet. It's a brand of dry vermouth made in France since the late 1800's that is often referred to as "the apèritif of Bordeaux". Bond's glassware of choice for the Vesper is a deep Champagne goblet.
The Vesper according to Ian Fleming and James Bond:
Three measures of Gordon's, one of vodka, half a measure of Kina Lillet. Shake it very well until it's ice-cold, then add a large thin slice of lemon peel. Got it?
-Casino Royale, Chapter 7