The stress test that stereophile uses to test amps is 1/3 rated power into an 8ohm simulated load.
I would bet that the LA II's would run at 4 ohm all day if you didn't push the volume too loud.
Your question to MB should be: at X percent of power of the amps into a 4 ohm load, how long will they play? or something like that.
So for example, the amps are rated at 180 into an 8 Ohm load. The stress test (stereophile runs them for 1 hour, then tests distortion and square waves etc..) would have them run at 60 watts into 8 Ohms.
So if your speakers are 88 db @ 1 watt, 1 meter effecient..
1 watt = 88 db
2 = 91
4 = 93
8 = 96
16 = 99
32 = 102
64 = 105
128 = 108
I really doubt you would want to listen at 88 db all day much less anything above 100 db.
If you do, then it is highly likely you already have hearing damage.
I would think it would be no problem for them to run at 1 watt into 4 Ohm all day.
Also if you will have them in an enclosed equipment case, they would get very hot running all day I would think. In an open rack with breathing room, I would think they would be OK. So there are many factors here for the questions you tried to raise.