Just saw some pics of people using hanging organizers to organize their makeup if they don't have room for bins / a vanity, and oh my god I am so impressed!!
You can try a basic organizer like this - usually made for jewelry or accessories, but totally perfect for makeup! You can see everything & it's easy to access.
Depending on how many lip products you have, you might need a shoe organizer just to hold all of your lipsticks!
If you want to get a bit fancier, you can buy one of these guys that opens and has a mirror on the front, but that's not as cheap or simple :D
They are also ones that have zippers you could get instead of one like these.
My only problem with this solution is that there isn't a mirror on it!!! I feel like if you had a mirror on it so you could do your makeup where you makeup IS, it would be totally perfect!