Is it true that I can only install app from app store in OS X Lion?
Can I not install app from any other source?
Not true - mean sure can install apps from dmg.
The Lion remain a full-blown OS, with all common functions, like Terminal.app, root access, Developer system, and so on. When here is no way block installing applications if you will have a root access, so Apple sure will NOT TRY do this.
The following is only my opinion:
On the other side - most of developers will sell their apps via AppStore (because it is easy), so here will be less "demo downloads" (what was possible activated by simple serial#). IMHO, over the time will be here more and more application in AppStore in two versions, like for example:
No, it's not true. Without breaking the NDA I can say, that many developers made their software Lion compatible and distribute it from their sites.