A potential auditory spatial cue, the envelope interaural time difference (ITDENV) is encoded in the lateral superior olive (LSO) of the brainstem. Here, we explore computationally modeled LSO neurons, in reflecting behavioral sensitivity to ITDENV. Transposed tones (half-wave rectified low-frequency tones, frequency-limited, then multiplying a high-frequency carrier) stimulate a bilateral auditory-periphery model driving each model LSO neuron, where electrical membrane impedance low-pass filters the inputs driven by amplitude-modulated sound, limiting the upper modulation rate for ITDENV sensitivity. Just-noticeable differences in ITDENV for model LSO neuronal populations, each distinct to reflect the LSO range in membrane frequency response, collectively reproduce the largest variation in ITDENV sensitivity across human listeners. At each stimulus carrier frequency (4-10 kHz) and modulation rate (32-800 Hz), the top-performing model population generally reflects top-range human performance. Model neurons of each speed are the top performers for a particular range of modulation rate. Off-frequency listening extends model ITDENV sensitivity above 500-Hz modulation, as sensitivity decreases with increasing modulation rate. With increasing carrier frequency, the combination of decreased top membrane speed and decreased number of model neurons capture decreasing human sensitivity to ITDENV.