This quote is about restraint, determination and willpower. In other words, it says "It's easy to not drink water if you're in the desert (because if you're thirsty, there is no water). But only a loyal/committed person would be able to resist drinking water in an oasis (an oasis is the opposite of a desert, it's a place with lots of water, grass, trees, etc.)
Another example is for a married man. "It's easy to be faithful to your wife if there are no other women available. But only a loyal husband will resist the temptation when there are other women available.
This is a very poetic statement. "sober" usually means when a person is not using alcohol or drugs. "part his lips" means "open his mouth" (to drink the water.)