We study changes of variable, called time transformations, which reduce a delay differential equation (DDE) with a variable non-vanishing delay and an unbounded lag function to another DDE with a constant delay. By using this reduction, we can easily obtain a superconvergent integration of the original equation, even in the case of a non-strictly-increasing lag function, and study the type of decay to zero of solutions of scalar linear non-autonomous equations with a strictly increasing lag function.