The traditional Chinese New Year menus are chosen to bring longevity, riches, peace, wisdom and virtue. Some of the most well-known foods:
- Fish -- the Chinese word for fish, yue, means abundance so fish bring good fortune and good health. Whole fish are luckier because cutting them up uses a knife or cleaver, which are unlucky implements. However, fish balls (or meat balls) with ingredients chopped before the holiday arrives are also traditional because of the round shape
- Lettuce -- the word "choy" for green vegetables also means good luck, and lettuce is the luckiest. Other greens like Chinese cabbage or broccoli also appear on New Year's menus. No word on the gangster use of "lettuce" to mean money.
- Foods representing "gold" -- foods to make you rich are gold in color (oranges, tangerines, pomelos, gourds) or resemble gold bars, especially dumplings or spring rolls. I find this interesting as in many European traditions, gold foods or even edible gold were popular for the same reason.
- Noodles -- are long, for long life. You have to eat them without cutting them, preferably by slurping.
I don't see much overlap with Valentine Day foods, though wearing red and decorations in red brings luck in Chinese tradition and is also the color for kids on Valentine's Day. Chocolate and heart-shaped candies are not particularly associated with Chinese menus, though there are sweets included in many of the feasts for the holiday.
Addendum: the Valentine Day and Chinese New Year timing is indeed unusual. According to the L.A.Times: "This is a rare convergence -- it's only the third time since 1900 -- and it won't happen again until after 2030."