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Line current differential (LCD) protection is traditionally considered to be highly dependable and secure. However, the increasing penetration of converter interfaced sources (CIS) (e.g. wind, PV, HVDC systems, etc.) could significantly reduce the system fault level and change the fault characteristics, thus presenting challenges to the reliable operation of LCD protection. In this paper, the impact of the integration of CIS on LCD performance is investigated comprehensively. Analytical expressions representing LCD relay operation in the presence of converter-driven fault currents and weak infeed conditions have been developed. A test network, comprising of a CIS model equipped with a typical converter fault-ride through strategy that is compliant with the GB Grid Code, has been built in a Real-Time Digital Simulator (RTDS). Simulations of LCD performance for different fault and system conditions are performed and presented. It is demonstrated that the dependability of the LCD relay can be compromised during internal phase-to-phase faults. The results also show that with the synchronous generation being displaced by CIS, the increasing CIS penetration and fault contribution from the CIS can lead to an increased phase angle difference between the fault currents contributed from the two ends of the protected line, which will increase the risk of the compromised protection performance.