Why fog and water have such a good relationship

Water holds heat longer than the ground around it, due to the fact that water  possesses a higher heat capacity than most land surfaces. Water's high heat capacity results from the relatively large amount of heat energy needed to break it's hydrogen bonds.

When cold air moves over warmer water, some of the relatively warmer water evaporates (water vapor) into the lower air layers immediately above the water surface. This now warmer air rises, mixes with the cooler air, which in turn creates condensation, and if it's dense enough, we call it fog.

Or the water surface may be colder (from up river or last night) than the road surface (warming in the sun) and cause water vapour in the air to condense into fog. Thanks to KalleMP for pointing this out.

First you must understand why condensation (in your case, in the form of fog) occurs at all. Fog is nothing but tiny $\textit{liquid}$ water droplets (usually less than 10 micron) that have condensed on to dust particles that are present in air. When water is present in vapor form in the air, it has a partial pressure associated with it. For any given partial pressure, there is associated a temperature known as saturation temperature, below which water cannot exist in the form of vapor alone, but has to condense on to any available surface. Now higher the water vapor concentration, which in its turn implies higher water vapor pressure, higher is the corresponding saturation temperature.

While the air temperature on both the road and the lake may be the same, water vapor concentration (and hence its partial pressure) is likely to be greater in the vicinity of a water surface such as over a lake than on the road, especially in conditions when there is negligible wind. If water vapor pressure in air above the lake is high enough that the corresponding saturation temperature is higher than air temperature, then you will see fog only there and not anywhere else. This is a possible explanation for what you observed.

A nice book I would recommend for you to read is $\textit{Clouds in a glass of beer}$ by Craig F. Bohren.