Sleep on the plane should match nighttime in your destination, not your origin. Otherwise the flight just extends your old time zone and the real adjustment starts only after you land.
Reset your watch to destination time at boarding. Sleep when it is night at the destination, even if it means staying awake the first few hours. Stay awake when it is day there, even if you are tired.
New York to London is a five-hour eastward shift. Sleep right after the meal service (around 02:00 London time), aim for four to five hours, get bright light on arrival.
London to Los Angeles is an eight-hour westward shift. Stay awake for the whole flight if possible — it is daytime in LA. A short nap before landing is fine.
Earplugs and an eye mask outperform any sleep aid. Skip alcohol. Hydrate. If you cannot fall asleep within 30 minutes, do not force it — read briefly with low light and try again.