Take a piece of thin card - fold into a concertina - stand on edge on a table. You can bend the concertina sideways very easily - you can squash the folds tighter fairly easily - but it is very hard to crush the card into the table.
So picking the right shape allows a material to have very different properties in different directions. The lyre has a long, convoluted suspension length which enables it to be exceptionally compliant (floppy) on the z-axis (the one that matters to the microphone diaphragm), but can behave more stiffly on the other axes to control the microphone from slopping around. Conventional elastic suspensions cannot provide this level of directional variation.
Physics dictates that all mechanical suspensions have a resonant frequency at which they amplify movement and only from about three times this frequency can they begin to isolate effectively. Thus good supensions should have a resonant frequency in the infrasonic range. Physics also confirms that all movements of a suspension will overshoot or "ring" and need to be damped to minimise this.
Take a guitar and slacken off one of the strings - the natural note moves down in frequency and becomes duller - it is more heavily damped.
The no-tension design of the lyre means that the suspension has a very low natural frequency and is heavily damped, something that no tensed elastic or spring suspension can match. The Hytrel material used can maintain this performance from arctic night to daytime desert temperatures.