Well, you knew I'd pipe in on this thread...
Actually, I'm not aware of any hard and fast rules about lip color and outfit color. I know that it used to be en vogue to color coordinate eyeshadows with your outfit but thankfully that trend is long gone (never to return, I hope).
I have a "standard" lip color that I wear 98% of the time--basically a neutral brownish/pinkish lip liner a few shades deeper and darker than my real lip color and I will swipe on a bit of neutral gloss on top for some shine. Then there's the 2% of the time when I decide to make my lips the focus of my look. The intent is not at all to "coordinate" with my outfit. To the contrary, it's usually when I'm wearing something dramatic and monochromatic that I choose to do a "strong lip" which usually means an "on trend" color such as this season's tomato red (but in a shade that works for me). In the alternative, I'll occasionally do a strong, smoky eye, which involves layering of various shades of shadow and liner to make my eyes stand out. I ALWAYS pair a smoky eye with a very neutral/nude lip to avoid the tranny look. That's probably the only "rule" I religiously follow in the make-up world.
I'm not sure these observations are helpful at all. I think part of why I suggested a neutral lip for you, Una, was thinking that it might be an easier look to carry off with a multitude of outfit colors. As much as I like a dark lip, I think it's hard to pull off for everyday wear.
One last thought: in terms of colors being more vs. less formal, in my mind, it has less to do with the color and far more to do with application. Although you might think that neutral eyeshadow colors, such as browns, plums and pale pinks might read "informal," you can definitely accomplish a very formal/dressy looking eye using those colors, provided you layer, layer and layer to create an intensity of color. It's a look I quite like, actually. Similarly, you can lightly sweep on some grey, dark green or deep blue shadows and make them work for day time. This is an area where make-up brushes are your best friend!