This is only a problem for enthusiasts, it seems.
I don't know why a few people are so offended by the fact that there is nothing more suitable to the Lymington Branch at the moment. As TEW has pointed out, there are actually quite a lot of services in Hampshire that are run by DMUs over wholly electric lines; this is just one of many. In fact, the arrival of the 456s will reduce these services, indirectly, by releasing 450s (which are already signed by crews down here so it's a lot simpler than sending some 456s). Perhaps we could release a 450 onto the Lymington branch, but to me that seems like a bit of a waste of capacity.
And before anyone in the north starts eyeing up the 158s and 159s that might be released by the 450s taking over the electric services, no you can't have them just now, SWT has already decided to allocate them for strengthening on the Salisbury line.