You can static-link in all of Qt. Just build Qt yourself. It can strip out all the things you don't need, even symbols from the libraries you do use, so your binary isn't going to be that big.
You can statically link Qt in compliance with the LGPL. The LGPL only requires that users are able to substitute the LGPL'd portion of an application with an alternative and compatible implementation.
Using a shared object/DLL is the traditional way of doing so, but you can also accomplish this by providing the object files for your application to allow users to link their own substitutions statically.
The FSF explicitly permits this as documented here:
You just have to open your source, that part which depends on Qt. It's not a real problem. But get a commercial license anyway, the cost is small compared to the other costs of developing your program, and you want to be friends with them.
(There's someone on HN who lives on a single-line modification of an open source program. Trust me, source availability of the source code of your client app won't really make a difference.)
He's a nice guy. If you want your company to buy his product, you send your boss a link to the product's home page (which doesn't say "open source") and tell your boss that this product is great. Your boss looks at the pricing and description, and says ok.
