Is it really crashing or just throwing up the 'unexpectedly quit' message? Earlier versions of PSE did this, too, in earlier versions of OS X. It's tedious but not important.
I don't have lion on this machine, but the first thing to try is to go to the equivalent of your username>library>preferences and delete:
Adobe Photoshop Elements 9 paths
Adobe Photoshop Elements 9 settings
opera prefernces (if you have them)
repair permissions and try again. In lion a lot of folders are now hidden, so it may not be so straightforward to find the path for those.
I'd also try installing java runtime as the kbase document suggests, if the suggestions in my first post don't do it.
Thanks for those answers.
I am right now at the photo trip thus have no access to my PC/
I will return to the office Monday - then I will try to gather some more information.
Tried removing those files, but no luck still crashes on exit. When it happened on Elements 8 I was told it was the TWAIN driver and I should remove it. I don't remember where that is now.
It can't be the twain driver in PSE 9 unless you specifically installed it, in which case it's in the PSE folder in applications>plug-ins>import/export. But that usually causes crashing on startup, not on exit.
PSE6 throws an expection while closing.
The fault log starts with (only smal excerpt)
Process: Adobe Photoshop Elements 
Path: /Applications/Adobe Photoshop Elements 9/Adobe Photoshop Elements.app/Contents/MacOS/Adobe Photoshop Elements
Version: 9.0 [20100905.m.9093] (9)
Code Type: X86 (Native)
Parent Process: launchd 
Date/Time: 2011-07-24 15:33:20.499 +0200
OS Version: Mac OS X 10.7 (11A511)
Report Version: 9
Sleep/Wake UUID: 979EC62A-0B15-4D4C-800F-FF570E39FCFA
Crashed Thread: 0 Dispatch queue: com.apple.main-thread
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0x000000002c4c5100
VM Regions Near 0x2c4c5100:
MALLOC_LARGE 000000002c100000-000000002c4af000 [ 3772K] rw-/rwx SM=PRV
MALLOC_TINY 000000002c500000-000000002c600000 [ 1024K] rw-/rwx SM=COW
Application Specific Information:
objc_msgSend() selector name: retain
objc: garbage collection is OFF
Thread 0 Crashed:: Dispatch queue: com.apple.main-thread
0 libobjc.A.dylib 0x9b63cd47 objc_msgSend + 23
1 com.apple.CoreFoundation 0x95a32868 CFRetain + 136
2 com.apple.CoreFoundation 0x95a7eb50 -[__NSArrayM insertObject:atIndex:] + 1024
3 com.apple.CoreFoundation 0x95a7e740 -[__NSArrayM addObject:] + 64
4 com.apple.AppKit 0x9216fcd8 -[NSApplication windows] + 254
5 com.apple.AppKit 0x921c88e3 -[NSPersistentUIManager flushAllChangesOptionallyWaitingUntilDone:updatingSnapshots:] + 451
6 com.apple.AppKit 0x921c86f6 -[NSPersistentUIManager flushPersistentStateAndClose:waitingUntilDone:] + 201
7 com.apple.HIToolbox 0x98ad4f08 _HIPersistentUIFlushPersistentStateAndClose + 240
8 com.apple.HIToolbox 0x98ac48d1 __EnsureBackingStoreCleanedAtExit_block_invoke_1 + 50
9 libsystem_c.dylib 0x9ace288a __cxa_finalize + 57
10 libsystem_c.dylib 0x9ace27f2 exit + 25
11 com.adobe.PhotoshopElements 0x000039ca _start + 224 (cvtas_get_scale.c:229)
12 com.adobe.PhotoshopElements 0x000038e9 start + 41 (cvtas_get_scale.c:196)
I have tried everything including reinstalling Java. This is a pain as
when I reload PSE it reloads the last photos worked on.
This crash report of course refers to PSE9 and not PSE6
No word ?
Try creating a new admin account and running PSE there. If it doesn't do it there, then the problem is a conflict with something in your user account.
It turns out to be my ONOne Essentials Plugin and possibly Portrait Professional.
Oh yes, OnOne does that. I think there's some kind of tech note on their site--not sure if they have a patch yet.
No patch yet, they are saying Oct.
Upgrading Portrait Professional Studio to 10.5 and removing OnOne Photo Essentials (3.0.3) solved the problem. Thanks.
BTW uninstalling PhotoEssentials with PP 10.1 still in system causes the problem.
I have to await OnOne patch...
I did that, and sometimes I am finishing a photo in Portrait Professional 10.5 and PSP crashes at the save point. So it can be a problem with PSP as well as Portrait pro Studio 10.5. I removed Essentials until the new vwersion arrives.