As it sounds, this treatment just brings HEAT and HUMIDITY, of course, and I don't think that we need more. Then, no, water does not dry out the skin, it would be a highest pitch.
I don't know how did your condition start but in my case, and I think this is a case of a lot of people here, by the pulling out of my lips, and it ends here. I know that I have no kind of infection or whatever and what I truly know is that chemicals are totally useless. -Also, I has never had eczema.-
As it still sounds, it is just steam so, yes, you also have steam when you are taking a shower but I don't think that you take about ten showers each day with a water as hot as the one which is ready to boil. Also, the simple fact to let the water-jet on your lips creates a pressure on the flakes which can not resist.
Regarding your lips condition, I think we all have the same symptoms and I don't know if you have already done a totally 'free' treatment but I think you would have the same state as mine in the first picture at the end of a month, of course it depends of your damaged area of your lips.
The steam treatment is not as using chemicals, at all, because by just applying chemicals on your lips your flakes would mechanically come off, by friction.
The steam enables the lips to catch the humidity that they need and heat enable the lips to take advantage of an optimal temperature to increase their productivity. Also, and it is very important, there is no friction at all, during a session.
As I said, you don't have to rub your lips, at all, but wait until they are well impregnated, then flakes will become dry again.