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More than three decades ago, it was noted that the ocean infragravity bound wave increasingly lags behind the forcing short-wave groups when propagating towards the shore. To date, the most recent theoretical prediction of this so-called phase lag remained a first-order approximation in terms of depth variations. Here, a new semi-analytical solution is proposed which does not rely on this approximation. Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions. This newly proposed theoretical phase lag is then extensively compared with the former one, highlighting an increasing discrepancy between the two solutions as the relative bottom slope increases. The four influencing parameters, namely the bottom slope, the water depth, the incident short-wave peak period and the incident group period, are shown to impact, each in a specific way, the bound wave phase lag. While the latter is seen to increase with lower water depths and/or with higher short-wave peak periods, both the bottom slope and the group period can affect the phase lag in a different manner. Indeed, steeper bed slopes induce lower phase lags in shallow water but higher ones in deep water, while higher group periods induce higher phase lags for gentle slopes but lower ones for steep slopes.