Completely wrong. You can definitely build closed-source applications with those IDEs. Their license means you cannot build proprietary IDE which INCORPORATES THEIR CODE. You could even build a your own proprietary IDE with those programs, so long as you wrote all the code yourself.
Since you are doing neither, their license is completely irrelevant. Use the IDE however you wish, the authors assert no copyright over your work.
Great! Brush up on licensing though. There is more than one way to license a program, some of which enable differnt business models.
In the DevDB, filter engines, libraries etc with the licenses 'MIT, BSD, ZLIB'. Anything licensed under those licenses is free for you to use, under the following conditions:
1) NO LAWSUITS!
2) NO DEFAMATION OR IMPLIED ENDORSEMENT! (It means don't say mean things about the authors or their work. The second part means don't claim the authors support your work, no "The OGRE3D Team Says My Game Really Shows Off Their Engine!!!" unless they actually said that and gave you permission to reprint)
3) GIVE CREDIT! (A simple 'Contains Software Copyright ' in a credits screen or README is generally enough, and not even technically required with the ZLIB license)
That's pretty much it. There are a couple finer points, especially if you use something under the Apache 2.0 license, but the principals are pretty much the same.
Do you mean using LGPL software, or licensing yours under LGPL? If the former, yes, you can use the software with a proprietary product, but it's pretty complicated so make sure you really understand what that license means, which is basically that you can interface with their DLLs, but you can't copy-paste their code implementations inside yours unless yours is GPL compatible as well (not just any open source license will do). If that sounds confusing, STAY AWAY!
If you want to license your software under LGPL, then yes, you can still sell it. You can even make it illegal to pirate by making the content proprietary but leaving the code open for modification. A very interesting business plan, one I hope to see more of in the future, but it may create confusion amongst the customers about the legality of redistribution. It can be very difficult the explain to people that they are only allowed to share the program itself and that sharing the complete game is actually piracy.
Hope that helps.
*** EDIT: Slight clarification on LGPL