[SalesForce] lightning Service Console: Open a standard record in lightning tab from a visualforce

I have a visualforce page inside my lightning Service console that displays related records of a case. On clicking on a record, I would like to open the detail in a new tab/subtab. For now, it opens in a separate window which is not in a lightning view. This is my vf page:

<apex:page showHeader="false" sidebar="false" standardController="Case" extensions="AssetRelatedListCtrl">
<apex:includeScript value="/support/console/40.0/integration.js"/>
<apex:form>
    <apex:pageBlock>
        <apex:selectList size="1" value="{!recordType}" style="width:130px;">
            <apex:selectOptions value="{!TypeOptions}"/>
            <apex:actionSupport id="recType" event="onchange" action="{!gatherRelatedAssets}" rerender="tablePanel"/>
        </apex:selectList>
        <apex:pageBlockTable value="{!relatedAssets}" var="asset" id="tablePanel">
            <apex:column headerValue="Id">
            <A HREF="#" onClick="openAssetSubtab('{!asset.Id}', '{!asset.Name}');return false">{!asset.Name}</A>
            </apex:column>
            <apex:column headerValue="Model" value="{!asset.Model__c}"/>
        </apex:pageBlockTable>
    </apex:pageBlock>
</apex:form>
<script type="text/javascript">
    var recordId = '{!caseId}';
    var assetId;
    var assetName;

    function openAssetSubtab(arg1, arg2) {
        assetId = arg1;
        assetName = arg2;
        if (sforce.console.isInConsole()) {
            sforce.console.getEnclosingPrimaryTabId(openSubtab);
        }else{
            OpenInNewTabWinBrowser('/'+assetId);
            //here, since im only using this page in the classic console and lightning console, I want to open the link in one or the other!
        }
    }

    function OpenInNewTabWinBrowser(url) {
        var win = window.open(url, '_blank');
        win.focus();
    }

    var openSubtab = function openSubtab(result) {
        var primaryTabId = result.id;
        sforce.console.openSubtab(primaryTabId , '/'+assetId, true, 
            assetName, null, openSuccess, 'salesforceSubtab');
    };

    var openSuccess = function openSuccess(result) {
        if (result.success == true) {
            console.log('subtab successfully opened');
        } else {
            console.log('subtab cannot be opened');
        }
    };
</script>