The only difference between the LMII and LMIII is the color of the knobs and the more fully featured DI on the LMIII. So, it is a 'slight freshening' of the LMII model. The LMTube is the more fully featured model that also has a second channel with combo jack input and separate gain control, a blendable tube pre (pretty subtle), and a push/pull mute on the master.
If you are one who uses a DI to record and/or play live, the added features of the LMIII DI are nice (level control, pre/post switch). If a DI is not that important to you (you can still switch the LMII DI to pre or post, but you have to take the top of the amp off and move a jumper), and/or you can get the original LMII at a discount, you will be happy with that model also.
Great amps IMO!