They are synonyms! And they are used more or less interchangeably. For the ocean, I would probably use "depth." Many people tend to use depth more often when you're asking for a measurement or some more exact information, while deepness is more about quality or something more metaphorical. However, it's a personal choice. Personally, I rarely use deepness, but use depth for most contexts. For "lack," the collocation is "lacking in." i.e. "Your saying is lacking in depth/deepness." Alternatively, "Your saying lacks depth/deepness"

'Do you know the depth of the ocean' is correct. Deepness isnt a word. 'Your saying is lacking depth' would be the best way to write that or 'What your saying lacks depth'