If you get this error you probably have database components set.
Try this:
1. Put libmysql.dll in your program's directory.
2. Make sure that bitness of your program matches bitness of libmysql.dll (i.e. if your program is 64 bit, libmysql.dll also has to be 64 bit)
That is if he's actually saved the Project there.
If he just fired up Lazarus, and entered some testcode, the dll in that place won't help him, since the scope the program is running in is the Lazarus-IDE itself,
(or maybe better said: the temporary "working directory" Lazarus created for the testrun. Not sure about that)