Diztronic is probably one of the thinnest cases with a mild lip without any huge designs or logos, save the right where their logo is printed on. too thin a lip and your screen may still come in contact with the surface, and assuming you want to avoid scratching it accidentally, this lip should be pretty welcome.
Rock supposedly has 0.6, 0.7, 0.8mm thick TPU cases but it may be hard to find and validate. Based on feedback from other users, you can probably look at ebay, amazon and hong kong/china if you want one. taobao is the chinese equivalent to ebay/amazon but if you can't read the strokes of the chinese characters, you should stick to ebay (proof: i can read chinese and i still have problems with their bombastic words).