A lake freezes first at its upper surface. Is convection involved? What about conduction and radiation?

Yes, convection is involved, but not conduction and radiation.
Convection is the mode of transmission of heat, through fluids, in which the particles of fluids acquire heat from one region and deliver the same to the other regions by leaving their mean positions and moving from one point to the other.
As the temperature of lake decreases, the density of water will decrease and it floats upward, lifted by the buoyant force whereas the high density water, at relatively higher temperature sinks in. That is why a lake freezes first at its upper surface. This circulation often develops naturally by the process of heat convection.