AIC = Amps Interrupting Capacity. The key word is Interrupting. That means interrupting a FAULT, not the normal day-to-day operations. A relay or any control device is not intended to interrupt a fault, that is the job of the OCPD; the fuse or breaker.
But in the course of day-to-day operation, if there is a fault on the down stream side of a control device, it will have to WITHSTAND the fault current until the OCPD can sense, react and interrupt the fault. That is (was) called the Withstand Rating, now it is called the SCCR (Short Circuit Current Rating) of the device since the release of the changes to Article 409 in the NEC a few years back.
So to that end, relays and anything else in a circuit must have an SCCR that is equal to or greater than the Available Fault Current (AFC) in a circuit. Generally, if a component or panel (such as an LCP) has not been specifically tested and listed with an SCCR, you have to assume it is rated for no more than 5kA. But if, in the case of most LCPs now offered by the major panelboard / breaker mfrs, the system is used with the mfrs own breakers, they typically will have been tested by them and listed to have an SCCR level the same as the OCPDs up stream. You have to check though.