<aura:component implements="force:hasRecordId,flexipage:availableForAllPageTypes"
access="global">
    <aura:handler name="change" value="{!v.recordId}" action="{!c.onRecordIdChange}"/>

<c:lwc_my_comp record-id="{!v.recordId}" ><c:lwc_my_comp>

</aura:component>

({
    onRecordIdChange : function(component, event, helper) {
        var newRecordId = component.get("v.recordId");
        console.log(newRecordId);
    }
})