try to do the following (before you install newer version)
open Terminal
cd /Developers/lazarus
cd lazarus.app/Contents/MacOS
./lazarus
also paste the results here.
Lazarus started.

But why can't I start it directly ?
Here is the result in the terminal (it's a bit long) :
TCarbonPrinter.ValidatePageFormat Error: PMSessionValidatePageFormat failed with result -30876
TMainIDE.ParseCmdLineOptions:
PrimaryConfigPath="/Users/user/.lazarus"
SecondaryConfigPath="/etc/lazarus"
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
NOTE: editor options config file not found - using defaults
NOTE: miscellaneous options file not found - using defaults
NOTE: codetools config file not found - using defaults
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
NOTE: help options config file not found - using defaults
TMainIDE.DoNewProject A
TFindDeclarationTool.ValidateToolDependencies project1.lpr
TFindDeclarationTool.ValidateToolDependencies project1.lpr
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCustomFormEditor.CreateComponent Form1:TForm1 True
TFindDeclarationTool.ValidateToolDependencies project1.lpr
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
TMainIDE.DoNewEditorFile END unit1.pas
TCarbonWindow.SetScrollInfo TODO
TCarbonWindow.SetScrollInfo TODO
There should be a Japanese Lazarus community. They might help you as well.
I don't know their site, but if you find out, please let me know.
I'm in Japan but I'm not japanese. I can read english better than japanese.
