Uhhh ... please don't continue to ask if I knew what was causing the problem!!! No, I don't ... but am trying to help you discover what the problem is so you can fix it. ;)
So the problem is still can;'t get to any admin area ... right? Let's leave debugging on as you might have found tip of an iceburg and there is yet other stuff that's not compat with 3.4 we've not discovered yet.
So let's review ... did the search and replace thing ... in-compat theme 'disappeared' (am wondering if it really did or not) ... so what's left is to get nasty ...
Not normally the first thing one would recommend but ... there is a table: mdl_config_plugins that contains the meta data for things like Lambda theme ... and including the theme actually exist. Is there 'lambda' folder in moodlecode/themes/ ... if so delete it.
Now the table ... can't tell you who lambda configs would be listed as in mdl_config_plugins, but since the folder is gone and the error you got said depreciated code ... we now need to eradicate any reference to that theme in mdl_config_plugins.
Use phpmyadmin for that ... enables you to see before you delete rows.
Then ... more nasty ...
In moodledata/cache/ remove all files folders.
in moodledata/localcache/ remove all files folders.
Clear your browser cache and cookies.
Did that do it?
'spirit of sharing', Ken