We propose a trimmed runs test for the hypothesis of symmetry with one sided alternative, in samples coming from the Generalized Lambda Distribution (GLD) with unknown median. We provide a method to calculate the exact distribution, showing that it is symmetric around zero and we give arguments to justify the approximation by means of the normal distribution. The size of the proposed test is calibrated with four symmetrical cases of the GLD and the empirical power is compared with that of some other tests for the same hypothesis, using eight asymmetrical cases of the GLD. The results show that the proposed test is unbiased in the cases used for calibration, and that the empirical power of the proposed test overtakes the empirical power of all compared tests, excepting one of them in two specific cases. Some hints are given concerning how to optimize the empirical power according to the size of the tails of the sampled distributions.