The term "lo mein" comes from the Cantonese lou mihn (撈麵), meaning "stirred/tossed noodles." In Mandarin, it's typically referred to as "拌麵 (mixed noodles)."
You can use the same type of noodles for lo mein and chow mien. Wheat noodles with egg is the typical type of noodles used in these dishes. Fresh egg noodles (preferably ~1/4" thick) are ideal for lo mein, while fresh or dried noodles can be used to make chow mein. With either, the noodles need to be softened via boiling before cooking. For dried noodles, it's recommended to parboiled in (boiling) water for ~5-6 mins before cooking, fresh egg noodles or the other hand only need ~2-3 mins. The necessary amount of cooking time will vary depending on the thickness of the noodles, so refer to the packaging for instructions.
You can refer to this guide as a reference to the different types of wheat noodles and their suitability in cooking.
The ultimate goal here is to boil them until they are just cooked, but not too soft (treat the noodles like pasta and cook them "al dente").
Cooking chow mein noodles involves to fry them into pancake of sorts, and then pouring stir-fried meat and vegetables over the fried noodles. This is similar to how Japanese yaki-soba is made, which is considered to be a derivation of chow mein, but with it's own unique distinction.
However with lo mein, the parboiled noodles are typically added near the end of cooking to be heat through (as opposed to bring fried) and tossed with a sauce and also tossed other ingredients (or have the ingredient poured over after the noodles have been tossed).
Contrary to what people say, when cooking chow mein, the noodles are fried separately albeit not to a crisp, but simply to coat it with oil and give it better texture. The frying stage is skipped when making lo mein. The crispiness of the noodles is not the distinctness that sets the two types of dishes apart.
What sauces you use and what ingredients you use it ultimately up to your tastes. Typically dark or light soy sauce, oyster sauce, chili sauce is used. Using sesame oil can help enhance the flavor of the dish with it's fragrant scent.
The second picture you posted (first after the edit) is "la mian." These types of noodles are more suitable for soup dishes, Japanese ramen is derived from these types of noodles for Japanese tastes as chuuka-soba.
The types of noodles noted in the last few images are called "fen si" (粉丝, the thin ones) and "fen tiao" (粉条, the flat ones). The former and latter is what is know as "cellophane/glass noodles/vermicelli." Both are typically made from mung beans or sweet potato starch. Both are usually stir-fried or served in soups and typically found in supermarkets in a dried form. The latter is usually thicker than the former.
While a distinction should be made between 粉丝 (fen si) and 米粉 (mi fen) is that mi fen is vermicelli made from ground rice, it's most likely that people will assume you mean the type with the bean/potato starch over the latter made from rice starch when you say "fen si".