What is the real difference in lo mein, chow mein, mei fun, and chop suey?
The problem with your question is that you're kind of asking something akin to "what is the universally accepted traditional preparation for Spaghetti". While conventionally in much of the English speaking world, that refers to spaghetti and meat sauce. The word/dish itself refers to a specific style/type of noodle and could be topped with anything.

Lo Mein and Chow Mein refer to the method of preparation and not the contents ("Stirred Noodle" and "Fried Noodle" respectively). They are both often wheat based egg noodles. Lo Mein is typically cooked in a broth, whereas Chow mein, by definition will be cooked in oil. Sometimes it'll be cooked till crispy, sometimes not.

If you happen to be in some location that serves authentic Chinese food, you could order dozens of different preparations for each of the above; It could include various combinations of proteins, vegetables. There are also different types of specific noodles used (eg: the small flat ones usually called "chow mein" in north american restaurants, larger round noodles often referred to as Shanghai Style Chow Mein, etc...). If I walked into a chinese restaurant in Hong Kong and asked for "Chow Mein" in Chinese, I imagine the response would most likely be, "what would you like on it?" Generally speaking there would be some protein and one or more vegetables. This is highly dependent on what is available locally. This varies greatly in China. Hong Kong will have access to more ingredients having been an international westernized port for a long time. The rest of China is more subject to local farming/fishing. That said, Seafood is very common in Hong Kong Cuisine given that it's a port. My friend from the north grew up with a lot more pork. But now my answer is becoming less about the dishes themselves.

Mei Fun means "Rice Noodle". Again, there is no accepted universal rule for what goes into it. My mom who comes from Hong Hong cooks those noodles half a dozen different ways depending on her mood.

Chop Suey like @Ching Chong said, just means "miscellaneous leftovers" or "assorted pieces". The origin is heavily debated and full of myth (see the wiki page). It is most commonly found these days from my understanding in Americanized Chinese restaurants in the US. I don't remember seeing it in Canada for example. Wherever it started, what makes it difficult to answer as it depends on what the cook wants to put in it. Anecdotally, I'm Canadian Chinese and have eaten at Chinese restaurants all over the world since I was born and have never actually ordered this dish, so take my answer for what it's worth. :-)