One problem with using the LGPL, is it assumes a more traditional environment where programs are compiled into object modules that are linked against system libraries. However, in the Arduino IDE environment, it doesn't use object modules, except for the base avr libraries, and the modules provided by the compiler. All of the additional Arduino stuff above the base libraries is recompiled each time from scratch. Now, you could arrange to use make and more traditional object modules to comply with the LGPL. However, given this, it might be simpler to just switch to a more traditional environment, and don't use the Arduino IDE as well.
Obviously, you have to go through each library that you use, to see what its copyright are, and either use it, or rewrite your own.