Para referência futura, o gksudo precisava ser adicionado ao arquivo .desktop, já que havia um problema com o Java, além de que aqui está o arquivo .desktop final que inicia o matlab no Lubuntu.
#!/usr/bin/env xdg-open
[Desktop Entry]
Type=Application
Icon=/usr/share/icons/matlab.png
Name=MATLAB
Comment=Start MATLAB - The Language of Technical Computing
#Uncomment the following line and comment the line after to
#force matlab to use the 32 bits architecture
#Exec=gksu -u root "/usr/local/MATLAB/R2013a_Student/bin/matlab -arch=glnx86 -desktop"
Exec=gksu -u root "/usr/local/MATLAB/R2013a_Student/bin/matlab -desktop"
Categories=Development;
#Uncomment the following line if you've got several matlab icons in the launcher
#StartupWMClass=com-mathworks-util-PostVMInit