Getting INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY when mocking an Object using Stub API

Question

I am mocking a routing rule object by using the JSON list below that has an ID of type Routing_Rule__c. The Test is about creating some rules and setting some flags that would cause the lead object to be set with the right rule. The Lead & Routing_Rule__c have a lookup relationship.

@isTest
    private static void testSomeStuff() {

//My mock data for Routing Rule
        String routingRulesListJSON = '[{"attributes":{"type":"Routing_Rule__c"},"Id":"a2h55000000Hh9uAAC","Routing_Target_Type__c":"Some Target","Start_Date_Time__c":"2020-03-01","Type__c":"New Lead","External_Id__c":"32","End_Date_Time__c":"2021-03-30","Execution_Order__c":"1"}]';
         List<Routing_Rule__c> routingRuleList = (List<Routing_Rule__c>)JSON.deserialize(routingRulesListJSON, List<Routing_Rule__c>.class);
         Routing_Rule__c routingRule = routingRuleList.get(0);     
         MockProvider.routingRuleList = routingRuleList;
         LeadRouting_Engine_Helper.routingRulesSelectorObj = (RoutingRuleSelector)MockUtil.createMock(RoutingRuleSelector.class);

        Account testAccount = [SELECT Id,Client_Practice_Status__c FROM Account WHERE Client_Practice_Status__c='Active'];       

        Test.startTest();
            Map<String,Object> leadMap = new Map<String,Object>();       
            leadMap.put('Client__c',testAccount.Id);
            Lead testLead = TestDataFactory.createLead(leadMap,TRUE);
            Lead newLead = [SELECT Id, Routing_Rule__c FROM Lead WHERE Id =: testLead.Id];

            system.assertEquals(routingRule.Id, newLead.Routing_Rule__c, 'Some Assert');
        Test.stopTest();
    }

When I run the following, I get :

System.DmlException: Insert failed. First exception on row 0; first error: INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY, insufficient access rights on cross-reference id: a2h55000000Hh9u: []

The issue is on line:

Lead testLead = TestDataFactory.createLead(leadMap,TRUE);

Which leads to:

public static lead createLead(Map<String, Object> fieldVars, Boolean doDml) {
        Integer i = leadCounter++;
        Lead l = new Lead(
                Company = 'Company'+i
        );
        if (fieldVars != null) {
            for (String key : fieldVars.keySet()) {
                l.put(key, fieldVars.get(key));
            }
        }
        if (doDml) insert l;
        return l;
    }

Which leads further to the Lead Trigger that has a piece of code that sets:

Lead.Routing_Rule__c = some-rule.Id;

When I comment out this line in the trigger, I have a failed assert but test executes. However I want that field to be set on the lead object for proper test scenario. I have tried using the full test under sys admin context but same error.

The test executes just fine when I do SOQL to create the Routing_Rule__c and get that ID but I feel the issue is with the ID and the fact that there is a lookup relationship so the system kind of wants an inserted data for routing rule prior to lead object being saved.

Is there a way I can proceed in my test that uses mocking or will I have to use traditional SOQL inserts in cases like this?