Highroller,
I don't know about your Lyr, but, a time delay mute is designed to prevent any output from the amp until it is warmed up and stable. Some tube gear will put out pretty nasty noise as it is powered up so a mute is designed to protect the speakers and your sensibilities while this is going on. The circuit does not necessarily also provide turn-on protection (soft start) for the amp itself; that is a separate feature. But, it is a good sign that the manufacturer is adding such features because soft start protection is even easier to implement.
I don't know about your Lyr, but, a time delay mute is designed to prevent any output from the amp until it is warmed up and stable. Some tube gear will put out pretty nasty noise as it is powered up so a mute is designed to protect the speakers and your sensibilities while this is going on. The circuit does not necessarily also provide turn-on protection (soft start) for the amp itself; that is a separate feature. But, it is a good sign that the manufacturer is adding such features because soft start protection is even easier to implement.