You would use an Anonymous Inner Class, as Java 8 lambda expressions are essentially syntatical sugar which do nearly the same thing. That would look something like this.
files.addAll(Arrays.asList(folder.listFiles(new FileFilter(){
@Override
public boolean accept(File f) {
return f.getName().endsWith(CustomConstantsRepository.FILE_EXT_DAT) && f.getName().startsWith(fileName)));
}
})));
solved File Lambda expression in Java 7