Yes. What you cannot do (without getting a commercial license) is make changes to Qt, without making those changes open source. So as long as you don't need to make a modified version of Qt for your app, you don't have to release anything.
This is a common LGPL misconception frequently seen.
IANAL, but even if you make a modified version of Qt and release it, you are still free to use that same modified version in your app without releasing it as open source, as long as you are using dynamic linking instead of static. But, the same restriction also apply to original Qt.
Btw, what you can't do is using modified version of Qt without releasing the source of your Qt modification upon request.
Just checking to make sure I understand right. The only piece you are adding is that the modified version needs to be released "upon request." Dagw also mentioned that Qt changes need to be open sourced to release an application using those modifications.