Place all of the ingredients in a cocktail shaker and shake with ice until frothy.
Strain to remove the ice then put everything back in the cocktail shaker and shake again before pouring into an (ideally chilled) coupe glass.
Notes
As noted in the post above, raspberry liqueurs and tastes vary, so you may want to hold back a little of the gin and the egg white, stir the other ingredients together then taste before deciding if you simply add the rest of the gin or also/instead a little more raspberry liqueur and/or lemon. I ended up using 25ml each of my homemade raspberry liqueur and lemon but that may be partly my taste. If you don't have Lillet blanc, while different my next choice would probably be a red vermouth.If you prefer, you can dry shake this by shaking first without ice then adding ice and shaking again. Both work, you just tend to get slightly more foam with adding ice first.