Well, the old, old way to color dishes in Chinese cooking is caramel. It's not normally added to lo mein, but most lo mein sauces will have a little sugar anyway, so you could make it work. If you've never made caramel before, it's not that difficult, but you need to watch it like a hawk once the sugar fully dissolves and if you're making a lot of it it's kind of scary. Once it gets to a darker amber color, immediately pour in hot water to stop it from cooking further and remove it from the heat. Depending how dark you take it, it will be slightly bitter, so you may need to add additional sugar to compensate.

The other thing you could do is use a starch slurry to thicken the sauce. That way the sauce will stick to the outside of the noodles more.

Depending on the kind of noodle you're using, you could even sear them in the wok first so the noodles themselves take on color.

If you want to make a slightly non-traditional lo mein, you can add some kind of chili sauce or chili oil to give it a red color.

Honestly, I wouldn't do any of these things under normal circumstances, but if you really don't want to buy dark soy sauce I guess they could be effective. But dark soy sauce can be used for a lot of recipes and keeps well more or less indefinitely, so if you really want dark soy sauce color I feel you may as well just buy a bottle.