A feature of matrix management is that this can lead to additional meetings, conference calls and emails and the proliferation of reporting and coordination mechanisms - this can make matrix management the opposite of lean (fat?)
Matrix organisation structures are a further step in creating a traditional hierarchy around what have become much more flexible ways of working, and may actually be counter productive.
The problem is that people management techniques developed for simpler times can make matrix management worse. Beyond a certain level of complexity more teamwork, meetings and conference calls make things worse. In matrix management we have to challenge these outdated assumptions in order to be both lean and matrixed.
It is not that matrix management is necessarily fat and wasteful, or that lean is always the best answer - it is about how we organize ourselves to be more effective.