While I’m not exactly sure about the source of your confusion, I think you are taking the relations a bit too far?
While low pressure works towards a higher density altitude, there’s nothing saying the pressure will be low if the density is low. You can have warm air at a high pressure and low density. The pressure depends more on the current weather pattern than anything else (except for altitude, obviously).
There’s also no direct relationship between altitude and temperature. Yes, the temperature of a rising parcel of air will drop with falling pressure (lapse rate) and the temperature will (typically) drop as altitude increases… but that’s only in one air mass at one time. Nothing says that it has to be colder at point A than at point B since point A is at a higher altitude. It is, however, perfectly possible and not uncommon to have a higher temperature at a higher altitude (inversion).
What is fixed is that the pressure will decrease with increasing altitude. The rate at which the pressure falls off with altitude is regulated by the air density though… which depends on temperature.
Perhaps it will be easier to sort out if you give us an idea of where you are going? What are you trying to sort out, what's the application?