This paper is concerned with the design problem of causal gain-scheduled output feedback controllers for linear parameter-varying systems using parameter-dependent Lyapunov functions. This research topic has already been addressed by several researchers, and several effective methods have been correspondingly proposed in terms of parametrically dependent matrix inequalities. This paper addresses the dual formulation of one of the methods, and successfully derives the counterpart result in continuous-time case but points out the intractability of deriving the counterpart result in discrete-time case. It is also shown, in discrete-time case, that the intractability disappears and a design method similar to an existing method is successfully derived if the causality with respect to scheduling parameters is abandoned, namely, if one-step ahead scheduling parameters are available. A toy example is introduced to confirm that, in continuous-time case, the derived dual formulation gives the same performance as the previously proposed method for the dual state-space representation of the example.