In this case, the equilibrium condition is characterized by the equality of the rates at which a process happen and the contrary process happen, so its ratio is 1. For instance, a chemical reaction at equilibrium will have a contant ratio of the velocity at which the products are formed and the reactants consumed
However, for the described insoluble solid that is allowed the reach equilibrium, the ratio of the rate at which ions join the solution and the rate at which ions join the lattice will be one since it reaches an equilibrium state.
When heat flows from one object or substance to another it is in contact with, the objects or substances are said to be in thermal contact. The state where objects in thermal contact with each other reach the same temperature, no heat flows between them.