I hate to break it to you, but if what's in the pic is all you have, you're nowhere near "done with the design." What you have is barely more than a napkin sketch, and a company like Lian Li won't take you seriously (and honestly, unless you're potentially worth a $100k+ annual contract to them, they won't be interested). Designing a case properly can take months of research, work, fine tuning, and testing. It's also helpful to have a solid background in building PCs, as well as at least a rudimentary understanding of airflow and thermodynamics.
If all you have is rough ideas (which is what it looks like), you can take it to Protocase and their engineers will work out it for you (for a price). That's what their company specializes in. Don't expect it to be cheap though; the more engineering hours they have to spend on it, the more it will cost. Expect it to be several thousand USD if you go that route.