OK, for starters lets assume you have these classes in module format. If not, then that should be the first order of business.
Second, avoid inheritance. There is almost always a better way to do it. Especially don't inherit across modules. About the only time I can think it's useful is for defaulting class parameters.
The base_dir on class app1 will not get the default unless the class inherits cea::params::base_dir (leading :: not needed). Again, across modules shouldn't be done. app1::params much better -- or just put in a sane default and eliminate the need to inherit parameters all together.
For your actual question, if you want to get a variable in another class you can just reference it. Keep in mind that puppet doesn't guarantee compile order so you should tell it to evaluate the other class first:
class executor::app {
Class['app1'] -> Class['executor::app']
$other_app_var = $app1::base_dir
}
Or throw this data in hiera and look up the value.