We perform group analysis of the second order linear differential equation with the most general variable time delay by developing a Lie type invariance condition using Taylors theorem for a function of more than one variable. This condition is then used to obtain the symmetry algebra and make a complete group classification of this delay differential equation. We deduce certain compatibility conditions for the infinitesimals which lead to an extension of the symmetry algebra. Finally, we obtain a change of variables leading the differential equation with variable delay to be reduced to a differential equation with constant delay.