I have faced same issue. I have found very simple solution. I may be late in answering but it can help someone in need.

Component:
`    <aura:attribute name="recordTypeIdVar" type="String"/>
    <lightning:recordEditForm aura:id="recordEditForm" 
                              objectApiName="Case"
                              recordId="{!v.recordId}" 
                              recordTypeId="{!v.recordTypeIdVar}"
                              onload="{!c.showRequiredFields}"
                              onsuccess="{!c.handleSuccess}">
                <h3 class="slds-section-title--divider">
                    <p>RecordType: {!v.recordTypeIdVar}</p>
                    <lightning:outputField fieldName="RecordTypeId"/> 
                </h3>`
blabla code here.. and close the component

Controller:
`showRequiredFields: function(component, event, helper){
       // To get the record type from URL as it is not happening by default.
        var recordTypeIdParam = helper.getJsonFromUrl().recordTypeId;
         //alert("recordTypeId= " + recordTypeIdParam);
        component.set("v.recordTypeIdVar", recordTypeIdParam);
    },` 

Helper:
`({
 getJsonFromUrl : function () {
        var query = location.search.substr(1);
        var result = {};
        query.split("&").forEach(function(part) {
            var item = part.split("=");
            result[item[0]] = decodeURIComponent(item[1]);
        });
        return result;
    }
})`