>>>I read that martagon lilies should best be moved when in full bloom.
Martagons seem to just take a lot longer to grow roots than most other lilies. And since annual stem roots are neglegible, martagons depend on basal roots for sustenance more than most lilies, too. It's likely you read that the best time is right after flowering, not during flowering. This is what Gene Fox writes in his book on martagons. He doesn't claim that this is the necessarily the best time for root growth, but rather, states that transplanting at this stage allows the time necessary for root re-establishment before winter. I have not seen any information that points to a specific time for martagon roots are more active, as there is for trilliums or crested iris, or some other types of plants, for instance. But, that doesn’t mean there is or is not a specific time for major martagon root growth. I just don’t know. However, I will say that it is not like some plants (i.e. daffodills or fritillaria), where root initiation only happens at certain times. For these plants, if that time is past, nothing can spur root gorwth. Martagons are definitely not that picky.
Of course, transplanting during active growth (like after flowering), means that greater care must be taken, in an attempt to keep the foliage alive and well. If however, the foliage does dieback because of transplant shock, that plant would still probably do better the following year, compare to if it was dug in the fall. Especially lilies of the martagon section (Ll. martagon, distichum, medeoloides, tsingtauense, hansonii), bulbs continue to grow underground even without any leaves above.
>>>I also read that the reason martagon lilies sometimes sprout in the spring just to suddenly die back is because they haven't rooted properly and therefore can't sustain the foliage?
That is the most common reason, and it can also be true of many other kinds of Lilium species and hybrids, too, not just martagons. Although, it does happen with martagons more often, simply because of the nature of the species.
