I think you should have told the folks that your Lyr amp is a headphone amp. Knowing this I think that you might have gotten different responses from folks had they known.
FWIW I see no fire hazard. None. The unit supposedly runs 'hot' but that is a relative term.
I see no need to turn off the unit except on a daily basis or after you are through using the unit each day. That way it will rest at least overnight. Small tubes typically have a long life.
I would not use different brands of tubes. Brands sound different and you would have the left channel with a different tone from the right channel if you don't use the same brand & type.
Turn down the volume to minimum when you turn off the unit. That should be enuf.
Re warm up - it doesn't take much time to warm up this type of unit. 5 to 10 minutes should be enough to take off any rough edges. If it takes more you will hear why when you listen. BTW, if you replace or roll tubes, be sure to get tubes tested for low noise.