Apple, in there "wisdom", has decided to drop gdb support with the arrival of MacOS X 10.9 (Mavericks) and XCode 5, gdb (GNU debugger) - which means that Lazarus user can no longer debug, which ... well sucks ...
A trick, originally posted in the Lazarus Forum, shows us that gdb of a previous XCode version can be used. However, downloading XCode 4.6.3 (1.7 Gb), installing and/or extracting the 2 needed files is cumbersome, so I adecided to post a ZIP file here with the 2 files (gdb and gdb-i386-apple-darwin).
After downloading you'll need to copy the 2 files in the right locations.
gdb has to be placed in
/usr/bin/
and gdb-i386-apple-darwin has to go into
/usr/libexec/gdb/
(you'll have to create the gdb folder in the libexec folder).
After copying the files in the right folders, start Lazarus and open the "Tools" - "Options...." menu.
Under "Debugger" - "General" you'll have to set "Debugger type and path" to "GNU debugger gdb" and the path to "/usr/bin/gdb" and you're good to go debugging Lazarus code even under MacOS X 10.9.
Caution:
Apple does not support older XCode versions on newer OS versions - so this trick might not work for your setup, and might stop working in future OS versions. On my MacBook Pro Retina however, this works great.