When liquids are classified using Tg-scaled Arrhenius plots of relaxation times (or relative rates of entropy increase above Tg) across a strong-fragile spectrum of behaviors, the strong liquids have always appeared rather uninteresting. Here we use updated plots of the same type for crystal phases of the rotator variety to confirm that the same pattern of behavior exists for these simpler (center of mass ordered) systems. However, in this case we can show that the strong systems owe their behavior to the existence of lambda-type order-disorder transitions at higher temperatures (directly observable in the cases where observations are not interrupted by prior melting). Furthermore, the same observation can be made for other systems in which the glass transition, at which the ordering is arrested, occurs in the thermodynamic ground state of the system. This prompts an enquiry into the behavior of strong liquids at high temperatures. Using the case of silica itself, we again find strong evidence from extended ion dynamics simulations, for a lambda transition at high temperatures, but only if pressure is adjusted to a critical value. In this case the lambda point is identifiable as a liquid-liquid critical point of the type suggested for supercooled water. We recognize the possibility of exploring, a postiori, the consequences of rapid cooling of laboratory liquid SiO2 from >5000K and multi-GPa pressures, using the phenomenology of damage-induced plasmas in optical fibers. The ramifications of these considerations will be explored to establish a big picture of the relation of thermodynamic transitions to supercooled liquid phenomenology.