Hi
The LSS decreases with increasing altitude not because of decreasing pressure, but because of decreasing temperature (as you may know the temperature gradient slopes towards colder temperature through the stratosphere and flips towards higher temperatures again up until the mesosphere).
You're right that we hit MMO before VMO at a constant IAS through altitude increase.
The TAS increases with increasing altitude at constant IAS because of decreasing density (roughly explained there is further between each air molecule, so for a constant IAS, dynamic air pressure, we "have" to have an increase in TAS; velocity in the particular body of air.)
So LSS is ONLY dependant on ambient temperature, thus the formula: LSS= 39 x the root of T (in kelvin).
Hope this somewhat clarifies the relationship between the different speeds.