It may be difficult to determine whether a dichotic lag-click points to the left or right when preceded by a diotic lead-click. Previous research suggests that this loss of spatial information is most prominent at inter-click intervals (ICIs) <10 ms. However, a study by Nilsson, Tirado, and Szychowska [(2019). J. Acoust. Soc. Am. 145, 512-524] found support for loss of spatial information in lag-clicks at much longer ICIs using a stimulus setup differing from those in previous research. The present study used a setup similar to that of the Nilsson, Tirado, and Szychowska study [(2019). J. Acoust. Soc. Am. 145, 512-524] to measure 13 listeners' ability to lateralize (left versus right) and detect (present versus absent) the lag-click in lead-lag click pairs with ICIs of 6-48 ms. The main finding was distinct individual differences in performance. Some listeners could lateralize lag-clicks all the way down to their detection threshold, whereas others had lateralization thresholds substantially higher than their detection thresholds, i.e., they could not lateralize lag-clicks that they could easily detect. Two such listeners trained for 30 days and managed to improve their lateralization thresholds to reach their detection thresholds, but only at longer ICIs (>20 ms), suggesting different mechanisms underlying lag-click lateralization at short versus long ICIs.