My understanding is that low pressure is usually associated with cloudy skies, however in the last week I observed a day that had low pressure reading but no clouds. Is this possible or did I perhaps read the barometer wrong?
Low pressure areas are simply areas where the air is less dense than the surrounding areas. The scale of these differences can be small, size of a small farm field, or large, covering expansive areas of the earth's surface.
Clouds form around low pressure systems typically because of the way low pressure systems develop and the air moves around them. Typically low pressure systems start forming over relatively warmer sections of the earth, this is gross over simplification, as the air warms it becomes less dense and will tend to rise. This rising of warm often moist air leads to cloud formation because as air rises it also becomes cooler, see Lapse Rate. Typically at some time the temperature drops below the dew point in the air moving upwards and clouds form. But if the relative humidity of the air is not high it is possible that the air mass in the low pressure system never rises high enough for condensation of the water vapor to occur, in this case no clouds will form.
In conclusion it is possible to read a lower air pressure at a site and still not have cloud formation.
This site has a good graphic on how low and high pressure systems relate to each other. High and Low weather systems described
Please note that I am not meteorologist. This answer does not consider all the aspects associated with cloud formation such as how airborne particulates can affect condensation
I'm not an expert, but my understanding is that you need moisture/humidity and nuclei around which water droplets can form.
I remember seeing a demonstration many years ago that showed this. There was a box about 12" per side with one side a rubber sheet and a few sides glass or plastic. They pulled the rubber sheet out (lowering the pressure) and nothing. They then lit and blew out a match inside the chamber. Closed the door, pulled the rubber sheet, viola a little cloud.
The soot provided the nuclei for the water droplets.